Answer
$\dfrac{3}{2(x-1)}$
Work Step by Step
Factoring the expressions and then cancelling common factors between the numerator and the denominator, then the given expression, $
\dfrac{9x+9}{4x+8}\cdot\dfrac{2x+4}{3x^2-3}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{9(x+1)}{4(x+2)}\cdot\dfrac{2(x+2)}{3(x^2-1)}
\\\\=
\dfrac{3\cdot\cancel{3}(\cancel{x+1})}{2\cdot\cancel{2}(\cancel{x+2})}\cdot\dfrac{\cancel{2}(\cancel{x+2})}{\cancel{3}(\cancel{x+1})(x-1)}
\\\\=
\dfrac{3}{2(x-1)}
.\end{array}
