\[\frac{16}{15} \cdot \frac{2}{5} - 6 \cdot \frac{1}{3} + 2 \frac{1}{12} \cdot \frac{4}{5} \]
\[= \frac{32}{75} - 2 + \frac{25}{12} \cdot \frac{4}{5} \]
\[= \frac{32}{75} - 2 + \frac{5}{3} \]
\[= \frac{32}{75} + \frac{5}{3} - 2 \]
\[= \frac{32}{75} + \frac{125}{75} - \frac{150}{75} \]
\[= \frac{32 + 125 - 150}{75} \]
\[= \frac{157 - 150}{75} = \frac{7}{75} \]