Answer
$\sqrt[6]{\dfrac{3a}{b^2-4}}$
Work Step by Step
Using $\sqrt[a]{x}\sqrt[a]{y}=\sqrt[a]{xy}$, the given expression, $
\sqrt[6]{\dfrac{a}{b-2}}\sqrt[6]{\dfrac{3}{b+2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[6]{\dfrac{a(3)}{(b-2)(b+2)}}
\\\\=
\sqrt[6]{\dfrac{3a}{b^2-2^2}}
\\\\=
\sqrt[6]{\dfrac{3a}{b^2-4}}
.\end{array}