Answer
$\dfrac{6}{a}$
Work Step by Step
The given expression, $
\dfrac{4a+8}{5a^2-20}\cdot\dfrac{3a^2-6a}{a+3}\div\dfrac{2a^2}{5a+15}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4a+8}{5a^2-20}\cdot\dfrac{3a^2-6a}{a+3}\cdot\dfrac{5a+15}{2a^2}
\\\\=
\dfrac{4(a+2)}{5(a^2-4)}\cdot\dfrac{3a(a-2)}{a+3}\cdot\dfrac{5(a+3)}{2a^2}
\\\\=
\dfrac{4(a+2)}{5(a+2)(a-2)}\cdot\dfrac{3a(a-2)}{a+3}\cdot\dfrac{5(a+3)}{2a^2}
\\\\=
\dfrac{\cancel{2}\cdot2(\cancel{a+2})}{\cancel{5}(\cancel{a+2})(\cancel{a-2})}\cdot\dfrac{3\cancel{a}(\cancel{a-2})}{\cancel{a+3}}\cdot\dfrac{\cancel{5}(\cancel{a+3})}{\cancel{2}\cancel{a}\cdot a}
\\\\=
\dfrac{6}{a}
.\end{array}
