(x - 4)(x - 12) ≤ 0
x2 - 16x + 48 ≤ 0
We know that either factor has to be 0 in order to have the left side equal 0, buuuuuut, to get the left side to be less than 0, the factors have to have opposite signs, or one has to be < 0 and the other > 0.
x2 - 16x + 48 < 0
(x - 12)(x - 4) < 0
x - 12 > 0
x > 12
x - 4 < 0
x < 4
To make Mark's point, we could also have...
x - 12 < 0
x < 12
x - 4 > 0
x > 4
That leads to 4 ≤ x ≥ 12, meaning that the solution is both that and your given solution, so an infinite number of solutions, but I think that's getting picky.
