\[\left( - 2\frac{2}{3} \right)b^{3}c^{2} \cdot \left( - \frac{9}{16} \right)b^{2}c^{2} =\]
\[= \frac{8}{3} \cdot \frac{9}{16}b^{5}c^{4} = 6b^{5}c^{4}.\]