Answer
$(2,4) \cup (6, \infty)$
Work Step by Step
$(x-6)(x-4)(x-2)\gt0$ Write as an equation.
$(x-6)(x-4)(x-2)=0$ Solve as an equation.
$x=6$
$x=4$
$x=2$
Plot these numbers on a number line,split them into intervals, take one test point from each interval, and check them to see if they are true. If they are true, then it is a solution.
In this case, it is
$(2,4) \cup (6, \infty)$