Upvote:5
There's no real way of knowing. You haven't even said what mode of transportation this reservation is by. Assuming an airline, there are two possible components:
Change fee. This is a fee the airline charges for making changes to your ticket. Many major US airlines have waived or eliminated these for many domestic flights, but that doesn't apply universally or sometimes to their cheapest "basic" fares. You can look up the change fee policy for your airline.
Difference in fare. Your new flight on the 14th may cost more if purchased now. It's a more short notice booking and seats may be scarce, so the airline may charge more. The airline will charge you this difference in fare. There's no way to know what this is without asking, as it depends on the airline's current prices for flights from Miami to New York City on July 14th. It's even possible the new fare will be less, and some airlines will give you back a credit toward future travel in this case.
The only way to know is to contact the airline (either by telephone or by using the "change your flight" feature of their website if available) and to price out different options, as it will depend on the fares available for each possible flight on the 14th.