To expand the left side of the equation, we need to multiply (x+6) by itself:

(x+6)(x+6) = x^2 + 6x + 6x + 36
= x^2 + 12x + 36

To expand the right side of the equation, we need to multiply (x-4) and (x+4), and then subtract 8:

(x-4)(x+4) - 8
= x^2 + 4x - 4x - 16 - 8
= x^2 - 24

Now, our equation becomes:

x^2 + 12x + 36 = x^2 - 24

Subtract x^2 from both sides:

12x + 36 = -24

Subtract 36 from both sides:

12x = -60

Divide by 12:

x = -5

Therefore, the solution to the equation is x = -5.