Answer
$\dfrac{4(a+9)(a+9)}{(a+2)(a-3)(a-2)}$
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+36}{a^2-7a-18}\div\dfrac{a^2-a-6}{a^2-81}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{4a+36}{a^2-7a-18}\cdot\dfrac{a^2-81}{a^2-a-6}
\\\\=
\dfrac{4(a+9)}{(a-9)(a+2)}\cdot\dfrac{(a+9)(a-9)}{(a-3)(a-2)}
\\\\=
\dfrac{4(a+9)}{(\cancel{a-9})(a+2)}\cdot\dfrac{(a+9)(\cancel{a-9})}{(a-3)(a-2)}
\\\\=
\dfrac{4(a+9)(a+9)}{(a+2)(a-3)(a-2)}
.\end{array}
