Answer
$\dfrac{3(x+2)^2}{5}$
Work Step by Step
Factoring the expressions and cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{3x^4-10x^2-8}{x-2}\cdot\dfrac{3x+6}{15x^2+10}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(3x^2+2)(x^2-4)}{x-2}\cdot\dfrac{3(x+2)}{5(3x^2+2)}
\\\\=
\dfrac{(3x^2+2)(x+2)(x-2)}{x-2}\cdot\dfrac{3(x+2)}{5(3x^2+2)}
\\\\=
\dfrac{(\cancel{3x^2+2})(x+2)(\cancel{x-2})}{\cancel{x-2}}\cdot\dfrac{3(x+2)}{5(\cancel{3x^2+2})}
\\\\=
\dfrac{3(x+2)^2}{5}
.\end{array}
