#### Answer

$x=-4$ or $x=4$

#### Work Step by Step

Using the definition of the absolute value, we have
$$\displaystyle
|x^2-16|=0
\\\Longrightarrow x^2-16=0\\
\Longrightarrow x^2=16
\\\Longrightarrow x=\pm\sqrt{16}
\\\Longrightarrow x=\pm4
$$
Thus, we have:
$x=4,$ or $x=-4$