\[x < 0:\ \]
\[\sqrt[4]{64x^{12}y^{8}} =\]
\[= \sqrt[4]{2^{4} \cdot 4 \cdot \left( x^{3} \right)^{4}\left( y^{2} \right)^{4}} =\]
\[= 2y^{2}\left| x^{3} \right|\sqrt[4]{4} = - 2\sqrt[4]{4}y^{2}x^{3}\]