The difference of four times a number and -8 is greater than -120. what is the solution set for the number?

It depends on how you look at the equation. There are 2 different ways to look at this problem.
First Method: 
4x-(-8)>-120
4x+8>-120
x>-32

Second Method:
-8-4x>-120
-4x>-112
x<28

***Most of the time, when people say the difference between two numbers they are asking for a positive integer. Therefore, I would suggest going with the second method.