Answer
$(0,-2)\cup(2,+\infty)$
Work Step by Step
$x^{3}-4x \gt0 \rightarrow x(x^{2}-4)\gt0 \rightarrow x(x-2)(x+2)\gt0$
These are zero when x=0, x=2,x=-2. These numbers divide the real line into the intervals $(-\infty,0)(0,-2)(-2,2)(2,+\infty)$
Using the test points to determine the sign of each factor in each interval: