Answer
$\frac{x+2}{2(x+3)}$.
Work Step by Step
The given expression is
$=\frac{3x^2-12}{x^2+2x-8}\div \frac{6x+18}{x+4}$
Invert the divisor and multiply.
$=\frac{3x^2-12}{x^2+2x-8}\cdot \frac{x+4}{6x+18}$
Factor.
$=\frac{3(x+2)(x-2)}{(x+4)(x-2)}\cdot \frac{x+4}{6(x+3)}$
Divide numerators and denominators by common factors.
$=\frac{x+2}{2(x+3)}$.
