Answer
$\dfrac{\sqrt[3]{6xy^2}}{2y^2}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{\sqrt[3]{3x}}{\sqrt[3]{4y^4}}
$ results to
\begin{array}{l}
\dfrac{\sqrt[3]{3x}}{\sqrt[3]{4y^4}}
\cdot
\dfrac{\sqrt[3]{2y^2}}{\sqrt[3]{2y^2}}
\\\\=
\dfrac{\sqrt[3]{6xy^2}}{\sqrt[3]{8y^6}}
\\\\=
\dfrac{\sqrt[3]{6xy^2}}{2y^2}
.\end{array}