Answer
Increasing on $(-2,0)\cup (2,\infty)$ and decreasing on $(-\infty,-2)\cup (0,2)$
Work Step by Step
See the graph of $f(x)=|x^4-16|$.
We can see that $f$ is increasing on $(-2,0)$ and $(2,\infty)$ and it is decreasing on $(-\infty,-2)$ and $(0,2)$.