Answer
$\dfrac{32a}{3(a+2)}$
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{4a^2-8a}{ab-2b+3a-6}\cdot\dfrac{8b+24}{3a+6}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4a(a-2)}{(ab-2b)+(3a-6)}\cdot\dfrac{8(b+3)}{3(a+2)}
\\\\=
\dfrac{4a(a-2)}{b(a-2)+3(a-2)}\cdot\dfrac{8(b+3)}{3(a+2)}
\\\\=
\dfrac{4a(\cancel{a-2})}{(\cancel{a-2})(\cancel{b+3})}\cdot\dfrac{8(\cancel{b+3})}{3(a+2)}
\\\\=
\dfrac{32a}{3(a+2)}
.\end{array}
