The second one:
You can easily find roots of f(x), i.e., x such that f(x) = 0. A product is zero iff at least one of the factors is 0. You can also determine whether f(x) is positive or negative between the roots by substituting some value between those roots for x. For example, when 0 < x < 6, we can take x = 1. Then we have: -x < 0, x + 2 > 0, (x + 9)^2 > 0, x - 6 < 0, i.e., there are two negative and two positive factors. All in all, f(x) > 0 when 0 < x < 6.
Note that f(x) has the same sign to the left and to the right of -9 because x + 9 occurs squared. For other roots, f(x) have opposite signs immediately to the left and to the right of those roots.