There's a few different ways to think about it; geometrically is likely easiest if you're already drawing the graph. First off, -4<x>2 is impossible. You have to say it the long way, which is "x > 2 OR x < -4".
The "> 0" part means it you want to take the region where this quadratic is positive. Think about the graph y = (x-2)(x+4): since it has a positive x^2 coefficient (as opposed to, say, -x^2 + 4x + 4) you should know that it is "nose-down" with a turning point below the x-axis and two branches that go up through it, marking your x-intercepts of (2, 0) and (-4, 0). These roots effectively cut the x-axis into three intervals, with the quadratic negative in the middle one and positive in the outer ones. So your solution is the "outside" combination of the root inequalities, namely x > 2 or x < -4.