Find all possible digits x, y, z such that the number 13xy45z is divisible
by 792.

I agree with Math Man's answer, but slightly simpler (I think) is the following:

If 13xy456 is divisible by 99, then it is divisible by 9 and by 11.

In order to be divisible by 9, x + y = 8 or 17

In order to be divisible by 11, x - y = -3 or 8

By inspection,

If x + y = 17, then x - y cannot be -3 or 8

If x + y = 8, then x - y cannot be -8

So, x+y = 8 = x-y

The only solution is x = 8, y = 0