\[2x\sqrt[6]{y} = - ( - x)\sqrt[6]{2^{6}} \cdot \sqrt[6]{y} =\]
\[= - \sqrt[6]{( - x)^{6}} \cdot \sqrt[6]{2^{6}y} =\]
\[= - \sqrt[6]{( - x)^{6} \cdot 64y} =\]
\[= - \sqrt[6]{64x^{6}y}\]