#### Answer

$2\sqrt[3]{a^{2}b^{}}$

#### Work Step by Step

Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression, $
\dfrac{\sqrt[3]{96a^4b^2}}{\sqrt[3]{12a^2b}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{96a^4b^2}}{\sqrt[3]{12a^2b}}
\\\\=
\sqrt[3]{\dfrac{96a^4b^2}{12a^2b}}
\\\\=
\sqrt[3]{8a^{4-2}b^{2-1}}
\\\\=
\sqrt[3]{8a^{2}b^{}}
.\end{array}
Extracting the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{8a^{2}b^{}}
\\\\=
\sqrt[3]{8\cdot a^{2}b^{}}
\\\\=
\sqrt[3]{(2)^3\cdot a^{2}b^{}}
\\\\=
2\sqrt[3]{a^{2}b^{}}
.\end{array}
Note that all variables are assumed to be positive.