\[- 4\frac{1}{6} \cdot \left( - 2\frac{2}{5} \right) = \frac{24 + 1}{6} \cdot \frac{10 + 2}{5} =\]
\[= \frac{25}{6} \cdot \frac{12}{5} = \frac{25 \cdot 12}{6 \cdot 5} = 10\]