Answer
$(-\infty,-4)U(4,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $x^2-16\gt0$
Step 2. Factor the quadratic, we have $(x+4)(x-4)\gt0$
Step 3. The boundary points are $x=-4$ and $x=4$
Step 4. Use test points at $x=-5, 0, 5$, the signs of the quadratic are $+, -, +$
Step 5. The inequality requires positive, thus the solution intervals (two outer regions) are $(-\infty,-4)U(4,\infty)$
