Answer
$\dfrac{8(a-2)}{3(a+2)}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $
\dfrac{8b+24}{3a+6}\div\dfrac{ab-2b+3a-6}{a^2-4a+4}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{8b+24}{3a+6}\cdot\dfrac{a^2-4a+4}{ab-2b+3a-6}
\\\\=
\dfrac{8(b+3)}{3(a+2)}\cdot\dfrac{(a-2)(a-2)}{(ab-2b)+(3a-6)}
\\\\=
\dfrac{8(b+3)}{3(a+2)}\cdot\dfrac{(a-2)(a-2)}{b(a-2)+3(a-2)}
\\\\=
\dfrac{8(b+3)}{3(a+2)}\cdot\dfrac{(a-2)(a-2)}{(a-2)(b+3)}
\\\\=
\dfrac{8(\cancel{b+3})}{3(a+2)}\cdot\dfrac{(\cancel{a-2})(a-2)}{(\cancel{a-2})(\cancel{b+3})}
\\\\=
\dfrac{8(a-2)}{3(a+2)}
.\end{array}
