To solve the equation given, we will first expand the expressions on both sides and then simplify:

(х+4)^2 - (х-2)(х+2) = 0

Expanding the left side:
(х+4)(х+4) - (х^2 + 2х - 2х - 4) = 0
(х^2 + 8х + 16) - (х^2 - 4) = 0
х^2 + 8х + 16 - х^2 + 4 = 0
8х + 20 = 0

Now, we will solve for x:
8х = -20
х = -20/8
х = -5/2

Therefore, the solution to the equation (х+4)^2 - (х-2)(х+2) = 0 is х = -5/2.