Expanding the expression:

(x+4)^2 - (x-2)(x+2)
= (x+4)(x+4) - (x^2 + 2x - 2x - 4)
= x^2 + 4x + 4x + 16 - x^2 - 4
= 8x + 12

Therefore, (x+4)^2 - (x-2)(x+2) simplifies to 8x + 12.