\[\frac{2x}{3}\ :\frac{3}{2x} \cdot \frac{9}{4xy}\ :\frac{x}{2y} =\]
\[= \frac{2x}{3} \cdot \frac{2x}{3} \cdot \frac{9}{4xy} \cdot \frac{2y}{x} =\]
\[= \frac{4x^{2} \cdot 9 \cdot 2y}{9 \cdot 4x^{2}y} = 2.\]