Answer
$\dfrac{(a+3)(a+1)}{a+2}$
Work Step by Step
The given expression, $
\dfrac{a^2-9}{a-6}\cdot\dfrac{a^2-5a-6}{a^2-a-6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(a+3)(a-3)}{a-6}\cdot\dfrac{(a-6)(a+1)}{(a-3)(a+2)}
\\\\=
\dfrac{(a+3)(\cancel{a-3})}{\cancel{a-6}}\cdot\dfrac{(\cancel{a-6})(a+1)}{(\cancel{a-3})(a+2)}
\\\\=
\dfrac{(a+3)(a+1)}{a+2}
.\end{array}
