I don't understand how to factor this question:

(x+y)^2 -64

The final answer is (x + y + 8) (x + y - 8).
I just don't understand how to get to that answer.

Recall: a^2-b^2 = (a+b)(a-b).

In your case: a^2 = (x+y)^2. b^2 = 64.
Factored: ((x+y)+8)((x+y)-8).