Answer
$=\displaystyle \frac{1}{3},\qquad x\neq 2,-3$
Work Step by Step
Factor what you can:
$x-2$ is factored
$3x+9=3(x+3)$
$2x+6=2(x+3)$
$2x-4=2(x-2)$
expression $=\displaystyle \frac{x-2}{3(x+3)}\cdot\frac{2(x+3)}{2(x-2)}\qquad$
...exclude the values that yield 0 in the denominator:
$x\neq 2,-3$
... cancel common factors: $2,\ (x-2)$, and $(x+3)$
$=\displaystyle \frac{1}{3},\qquad x\neq 2,-3$
