\[\frac{9x^{6}}{y^{3}}\ :\frac{6x^{4}}{y^{5}} = \frac{9x^{6} \cdot y^{5}}{y^{3} \cdot 6x^{4}} =\]
\[= \frac{3x^{2}y^{2}}{2} = 1,5x^{2}y^{2}.\]