[tex]\sqrt[3]{\dfrac{x^3}{cy^4}}=\dfrac{x}{4y\sqrt[3]{y}}\\\\\\\dfrac{\sqrt[3]{x^3}}{\sqrt[3]{cy^3\cdot y}}=\dfrac{x}{4y\sqrt[3]{y}}\\\\\\\dfrac{x}{y\sqrt[3]{cy}}=\dfrac{x}{4y\sqrt[3]{y}}\\\\\\\sqrt[3]{cy}=4\sqrt[3]{y}\\\\\sqrt[3]{c}\sqrt[3]{y}=4\sqrt[3]{y}\\\\\sqrt[3]{c}=4\qquad|(\ldots)^3\\\\c=4^3\\\\\boxed{c=64}[/tex]
Answer D.
