\[3\frac{3}{7}x^{5}y^{6} \cdot \left( - 2\frac{1}{3}x^{5}y \right)^{2} = \frac{24}{7}x^{5}y^{6} \cdot\]
\[\cdot \left( - \frac{7}{3} \right)^{2}x^{5 \cdot 2}y^{2} = \frac{24 \cdot 49}{7 \cdot 9}x^{5 + 10}y^{6 + 2} =\]
\[= \frac{56}{3}x^{15}y^{8} = 18\frac{2}{3}x^{15}y^{8}\]