Answer
The inequality is valid on values less than 0 and more than 4 (not including them) i.e. $(-\infty,0)\cap (4,\infty)$
Work Step by Step
First, we are going to set the right side to zero and factor to find the x-intercepts:
$x^2-4x$
$x(x-4)$
$x_1=0$
$x_2=4$
These are the critical points. We are going to take three values: one less than 0, one between 0 and 4, and one more than 4 to test in the original equation and check if the inequality is true or not:
First test with a value less than 0:
$(-1)^2-4(-1)>0$
$1+4>0$
$5>0 \rightarrow \text{ TRUE}$
Second test with a value between 0 and 4:
$1^2-4(1)>0$
$1-4>0$
$-3>0 \rightarrow \text{ FALSE}$
Third test with a value more than 4:
$5^2-4(5)>0$
$25-20>0$
$5>0 \rightarrow \text{ TRUE}$
These tests show that the inequality $x^2-4x>0$ is valid on values less than 0 and more than 4 (not including them) i.e. $(-\infty,0)\cap (4,\infty)$