Answer
$\dfrac{2}{r+2}$
Work Step by Step
The given expression, $
\dfrac{6r-18}{9r^2+6r-24}\div\dfrac{4r-12}{12r-16}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{6r-18}{9r^2+6r-24}\cdot\dfrac{12r-16}{4r-12}
\\\\=
\dfrac{6(r-3)}{(3r-4)(3r+6)}\cdot\dfrac{4(3r-4)}{4(r-3)}
\\\\=
\dfrac{6(\cancel{r-3})}{(\cancel{3r-4})(3r+6)}\cdot\dfrac{\cancel{4}(\cancel{3r-4})}{\cancel{4}(\cancel{r-3})}
\\\\=
\dfrac{6}{3r+6}
\\\\=
\dfrac{6}{3(r+2)}
\\\\=
\dfrac{\cancel{3}(2)}{\cancel{3}(r+2)}
\\\\=
\dfrac{2}{r+2}
.\end{array}
