\[\sqrt[4]{48x^{8}y^{4}} =\]
\[= \sqrt[4]{2^{4} \cdot 3 \cdot \left( x^{2} \right)^{4} \cdot y^{4}} =\]
\[= 2x^{2}|y|\sqrt[4]{3} = - 2\sqrt[4]{3}x^{2}y\]