Answer
$\dfrac{2\sqrt[3]{x^2y}}{x}$
Work Step by Step
RECALL:
$\dfrac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\dfrac{a}{b}}.$
Use the rule above to have
$\require{cancel}
\sqrt[3]{\dfrac{48x^3y^2}{6x^4y}}
\\=\sqrt[3]{\dfrac{\cancel{48}8\cancel{x^3}x^2\cancel{y^2}y}{\cancel{6}\cancel{x^4}x^3\cancel{y}}}
\\=\sqrt[3]{\dfrac{8x^2y}{x^3}}
\\=\sqrt[3]{\dfrac{2^3x^2y}{x^3}}
\\=\dfrac{2}{x} \cdot \sqrt[3]{x^2y}
\\=\dfrac{2\sqrt[3]{x^2y}}{x}.$
