\[y < 0:\]
\[3y\sqrt[6]{x} = - ( - y)\sqrt[6]{3^{6}}\sqrt[6]{x} =\]
\[= - \sqrt[6]{( - y)^{6}} \cdot \sqrt[6]{3^{6} \cdot x} =\]
\[= - \sqrt[6]{( - y)^{6} \cdot 3^{6}x} =\]
\[= - \sqrt[6]{729xy^{6}}\]