\[\frac{16x^{3}}{9y^{4}}\ :\frac{8x^{8}}{27y^{6}} = \frac{16x^{3} \cdot 27y^{6}}{9y^{4} \cdot 8x^{8}} =\]
\[= \frac{6y^{2}}{x^{5}}\]