Why does Nephi believe he can keep all the commandments?

GOD because of the GRACE of the LORD JESUS - doesn't see you as sinful.

HE became sin on the cross. 2nd Corinthians 5:21

And GOD not counting man's sins against us. 2nd Corinthians 5:19

So, its only in seeing us as HE see's us, a righteousness by faith as scripture clearly tells, that we are blameless and holy. see Romans 3:22

It boils down to either a righteousness by our own doing. We go to church, pray, fast, tithe, do this and do that…banking on our own religiousness (righteousness). OR we rather seek HIS kingdom and HIS righteousness only to have everything added to us. (rather than everything lost)

So, we CANT keep the commandments or laws - impossible. How do we keep them then? by Grace. Seeing and experiencing GOD coming on the inside of us, making us lovers/servers not takers and manipulators. When HE places (by us just thanking HIM for it) that love on the inside. We start to walk better.

But again we are only HOLY or Righteous by taking what JESUS has done as our own - even though we don't deserve it. Otherwise it wouldn't be GRACE.

-ezeric

The answer is in his own strength.

Your ability to resist temptation is measured by spiritual strength. The stronger your spirit, the easier it is to keep the commandments and abhor evil.

Just like your body requires constant nourishment and exercise for physical strength, your spirit also requires constant nourishment and exercise for spiritual strength.

Nephi was diligent in nourishing his spirit, which kept his faith strong:

And it came to pass that after I had received strength I spake unto my brethren, desiring to know of them the cause of their disputations. (1 Nephi 15:6)

Read Dallin H. Oaks devotional address on Nourishing the Spirit to learn more about how you can strengthen your spirit.

Nephi was not perfect in keeping the commandments. In fact, in 2 Nephi 4 he cries out:

17 Nevertheless, notwithstanding the great goodness of the Lord, in showing me his great and marvelous works, my heart exclaimeth: O wretched man that I am! Yea, my heart sorroweth because of my flesh; my soul grieveth because of mine iniquities.

18 I am encompassed about, because of the temptations and the sins which do so easily beset me.

19 And when I desire to rejoice, my heart groaneth because of my sins; nevertheless, I know in whom I have trusted.

(Emphasis added.) What follows is the beautiful Psalm of Nephi (2 Nephi 4:17-35) in which Nephi praises the Lord for his goodness and mercy and affirms his commitment to follow the Savior. Every commandment can be obeyed, but we fail again and again to keep all the commandments all the time. Yet, we can be perfected through the grace of Christ and his atonement as Moroni states in Moroni 10:

32 Yea, come unto Christ, and be perfected in him, and deny yourselves of all ungodliness; and if ye shall deny yourselves of all ungodliness, and love God with all your might, mind and strength, then is his grace sufficient for you, that by his grace ye may be perfect in Christ; and if by the grace of God ye are perfect in Christ, ye can in nowise deny the power of God.

33 And again, if ye by the grace of God are perfect in Christ, and deny not his power, then are ye sanctified in Christ by the grace of God, through the shedding of the blood of Christ, which is in the covenant of the Father unto the remission of your sins, that ye become holy, without spot.

(Emphasis added.) It is evident from the scriptures, that all have sinned, and come short of the glory of God (Romans 3:23). It is natural for men, to fail keeping the commandments (Mosiah 3:19), and God does not expect us to keep all commandments all the time perfectly. Jesus has done that work for us. What he asks us to do, is to do the best to keep his commandments and repent whenever we fail. Patience and perseverance in trying to do your best are much more important than beating oneself up over every little thing you do wrong (see Alma 42:29; 2 Cor 7:10). Yet we have the promise that

God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it. (1 Cor 10:13)

(See also Alma 13:28.) Hence, we can overcome every sin through God's grace. All he asks us is to try the best we can and whenever we fail, to try again and continue. There's an excellent talk at BYU by Brad Wilcox about the topic of grace which explains this really well.