In this question we are given an equation containing the variable x. Upon seeing the question, we may think that we are asked to solve for x from the first equation, (x + 4)3 = 0, but it doesn't end there. We will be using this value of x from the first equation to evaluate the second one: (x − 2)(x + 6).

The given equation is
(x + 4)3 = 0
which means, (x + 4) is some number which, when cubed, produces zero! This is possible only if the term itself equals zero:
x + 4 = 0
and, therefore,
x = −4
Let us now plug this value of x into the expression to be evaluated.
(x − 2)(x + 6) = (−4 − 2)(−4 + 6) = (−6)(2) = −12

The correct answer is (A).