Answer
$$|2x^3|$$
Work Step by Step
RECALL:
(1) If $n$ is odd, then $\sqrt[n]{a^n}=a$.
(2) If $n$ is even, then $\sqrt[n]{a^n} = |a|$
Use rule (2) above to obtain:
\begin{align*}
\sqrt[4]{16x^{12}}&=\sqrt[4]{(2x^3)(2x^3)(2x^3)(2x^3)}\\
&=\sqrt[4]{(2x^3)^4}\\
&=|2x^3|
\end{align*}