By having a bug in the code. 4,294,967,295 is equal to 0xFFFFFFFF in hexadecimal, which is the 4-byte two's complement representation of -1. ETA:...come to think of it, it's also the 4 byte result of unsigned subtraction of 1 from 0.
Or else it's a 4 byte unsigned value and someone just figured out a way to max out their thanks.
It is a bug, I doubt there's anything you can do as a user to cause it- it's probably the result of admins deleting posts causing thanks to be removed twice or something like that. You'd need admin access and if you had admin access you could just set your thanks to whatever you want anyway.