Answer
$\dfrac{x+2}{2(x+3)}$
Work Step by Step
The given expression, $
\dfrac{3x^2-12}{x^2+2x-8}\div\dfrac{6x+18}{x+4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{3x^2-12}{x^2+2x-8}\cdot\dfrac{x+4}{6x+18}
\\\\=
\dfrac{3(x^2-4)}{(x+4)(x-2)}\cdot\dfrac{x+4}{6(x+3)}
\\\\=
\dfrac{3(x+2)(x-2)}{(x+4)(x-2)}\cdot\dfrac{x+4}{6(x+3)}
\\\\=
\dfrac{\cancel{3}(x+2)(\cancel{x-2})}{(\cancel{x+4})(\cancel{x-2})}\cdot\dfrac{\cancel{x+4}}{\cancel{3}\cdot2(x+3)}
\\\\=
\dfrac{x+2}{2(x+3)}
.\end{array}
