Answer
$\dfrac{x+2}{x+3}$
Work Step by Step
Factoring the expressions and then cancelling common factors between the numerator and the denominator, then the given expression, $
\dfrac{2x^3-16}{6x^2+6x-36}\cdot\dfrac{9x+18}{3x^2+6x+12}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2(x^3-8)}{6(x^2+x-6)} \cdot\dfrac{9(x+2)}{3(x^2+2x+4)}
\\\\=
\dfrac{\cancel{2}(\cancel{x-2})(\cancel{x^2+2x+4})}{\cancel{2}\cdot\cancel{3}(x+3)(\cancel{x-2})} \cdot\dfrac{\cancel{3}\cdot\cancel{3}(x+2)}{\cancel{3}(\cancel{x^2+2x+4})}
\\\\=
\dfrac{x+2}{x+3}
.\end{array}
