What is the basis for the idea of 7,000 years of human history, expressed by Larkin and others?

What is the basis for the idea of 7,000 years of human history, expressed by Larkin and others?

It should be noted that while this is the predominant position of most of protestant Christianity, many who hold this view do not like or use the term YEC, [Young Earth Creationist].
This is also true of one of the most well-known and respected teachers, Ken Ham, who says that anything that is 6000- 10,000 years is ancient, not young. So a more accurate term is Literal Biblical Creationist.

• They hold that the creation account of an ancient earth is literal, approx 6,000 to 10,000 years, and there is Biblical support for this outside Genesis, as well as extra-Biblical support for this. One of the basic principles of Hermeneutics [Biblical Interpretation] is that "Scripture Interprets or sheds light on other scripture" - Examine what other passages say about the same topic. Is there support for this by multiple writers and across multiple genres - as opposed to it only being found in a passage of poetry or wisdom literature?
• First, we have to start with the context. Genesis is part of the Pentateuch, [Literally means 5 books] and is classified as the Torah, which is the Hebrew word for Law. A widespread convention used by many translators through history is dividing the Old Testament into 3 groups or categories. History, Poetry/Wisdom and Prophets. What is significant is that Genesis is classified as History along with Judges, 1 & 2 Chronicles, Ruth and Esther. Even secular experts on Hebrew agree that the style of Genesis is narrative, and that it is not like other books of poetry like Psalms, or Proverbs, which uses symbolism and allegory and metaphors. https://creation.com/is-genesis-poetry-figurative-a-theological-argument-polemic-and-thus-not-history The Hebrew word for day is "yom" and in fact sometimes can be used in the sense of 'eras' or epochs, but in this passage the text explicitly says that the days were each defined with an evening and a morning. The evening and the morning were the first day, second day, third day, etc.
  Furthermore, the Biblical creation account states God rested on the 7th day, and this is the model for the 7th day of rest which is the Sabbath. It makes no sense whatsoever to have 6 unknown indefinite periods of work followed by another unknown, indefinite period of rest.
  How could anyone know how long the periods of work were to be? So they must work for 6 months straight, and then rest for one month? The notion that these were long epochs becomes even more absurd the longer the time period goes -so mankind is supposed to work for 6 years straight and then have a year or rest, or sixty years of work, followed by ten years of rest.
  https://creation.com/one-day-is-as-a-thousand-years-warning

In addition, each day of creation in Genesis 1 is marked by ‘evening’ and ‘morning’, so it is impossible to stretch the days out to millions of years on Earth. (See: The numbering pattern of Genesis for a more in-depth analysis of the Hebrew syntax in this regard). The days in Genesis 1 are clearly a reference to man’s time—or more specifically, a literal day on Earth—marked by an evening and a morning. Continuing contradictions The order of creation in the Bible contradicts the evolutionary order in over two dozen places, and stretching the days out into long periods of time only makes the matter worse. For example, the Bible tells us that the plants were created on Day 3, but the sun, moon and stars were created on Day 4. Aside from the plain, common sense reading of literal days, each one being defined by an evening and a morning, is there any other evidence from scripture, and outside of scripture? Yes and Yes!

This is a very important passage and is almost always overlooked, but the significance cannot be overstated. Genesis 6:3 NIV 3 Then the Lord said, “My Spirit will not contend with humans forever, for they are mortal; their days will be a hundred and twenty years.”

• 1. "One theory is that God notified Noah of the coming flood 120 years before it happened. There are all sorts of difficulties with this theory including the simple fact that it is impossible to verify. There is no biblical evidence to support that it happened. It was never cited as a fulfilled prophetic utterance."
• 2. Another theory is that God was limiting the lifespan of man to 120 years. The difficulty with this theory is that it does not match up with reality. Obviously, this theory is not supported by the genealogies and lifespans recorded in the bible. The lifespan of man has never matched up with this theory. Men and women lived for hundreds of years after the flood. Even today there are example of men living over 120 years in a world where depending on where you live the lifespan of man is between 70-80 years."
     http://livingwordin3d.com/discovery/2017/04/30/the-mystery-of-the-120-years/

The 120 years in the passage is 120 Jubilee cycles. [Each Jubilee cycle is 50 years] 120 x 50 = 6000 years. So this puts the days of Humanity as 6000 years, plus the Sabbath rest of the 1000 year millennial reign of Christ as recorded in Revelation as 7000 years.

Rev 20:3-6 3. The angel then threw him into the abyss and locked and sealed it so that he could not deceive the nations until the one thousand years were finished. (After these things he must be released for a brief period of time.) 6 Blessed and holy is the one who takes part[m] in the first resurrection. The second death has no power over them, but they will be priests of God and of Christ, and they will reign with him for a thousand years.

Then, we also see the concept of the earth being several thousands of years in the Jewish calendar which is used by tens of millions of religious and secular Jews around the world. This is because the Jewish scholars understood the geneologies in the Tanakh - What Protestants call the Old Testament to be literal.
So even those Jewish secular scholars who reject the New Testament, and may not be religious say that the current year on the Jewish calendar is 5781. https://www.science.co.il/israel/holidays/#:~:text=In%20the%20Hebrew%20calendar%2C%20a,5781%20(%D7%AA%D7%A9%D7%A4%22%D7%90).

To supplement the existing answer, perhaps the earliest Christian exposition on the idea of a 7000-year history corresponding to the seven days of the creation week is found in the Epistle of Barnabas, written in the early- to mid-second century AD.

In chapter 15, the author reinterprets the first six days of Genesis 1 as an allegory for six-thousand years of history (with the author believing he was living near the end of that sixth millennium).

Listen, children, what this means: "He finished in six days." He means this, that in six-thousand years the Lord shall finish all things. For a day with him is like a thousand years, and he testifies to this, saying: "Behold, the day of the Lord shall be as a thousand years." Therefore, children, in six days, that is in six thousand years, everything shall come to an end.

He then anticipates these six 'days' to be followed by a seventh 'day' Sabbath rest, i.e. a thousand years of rest brought on by the second coming of Jesus:

"And he rested on the seventh day." By this he means, when his son comes, and abolishes the time of the lawless one, and judges the ungodly, and changes the sun and the moon and the stars, then shall he truly rest on the seventh day.

At first the author seems to describe this seventh 'day' Sabbath as lasting forever, using ideas that typically are reserved for the new creation (e.g. describing this seventh millennium as the time 'when iniquity is no more and all things have been made new by the Lord'). Sticking strictly to the creation week of Genesis 1-2, this would seem appropriate. But then the author alters the formula by adding in an eighth millennium, basing the idea on Jesus' resurrection on the the 'eighth day' of the week (i.e. Sunday, the day after the seventh day Sabbath).

Finally he says to them: "Your new moons and your Sabbaths I cannot endure." You see his meaning: Your present Sabbaths are unacceptable to me, but in the Sabbath I have made, when I have set all things to rest, I will make the beginning of the eighth day, that is, the beginning of another world. Wherefore, also, we keep the eighth day with joyfulness, the day when Jesus rose again from the dead too.

(Textually, there is no evidence Barnabas was relying on Revelation 20 in his anticipation of a future thousand-year rule of Jesus.)