\[\left( \frac{2}{3}xy^{2} \right)^{3} \cdot \frac{3}{2}x^{3}y^{2} =\]
\[= \frac{8}{27} \cdot \frac{3}{2} \cdot x^{3}y^{6} \cdot x^{3}y^{2} = \frac{4}{9}x^{6}y^{8}.\]