To solve the expression \( 15 \left( \frac{1}{5} 2 - 8 \cdot \frac{1}{5} \right) \), we can follow these steps:
Calculate \( \frac{1}{5} \cdot 2 \): \[ \frac{1}{5} \cdot 2 = \frac{2}{5} \]
Calculate \( 8 \cdot \frac{1}{5} \): \[ 8 \cdot \frac{1}{5} = \frac{8}{5} \]
Now substitute these values back into the expression: \[ 15 \left( \frac{2}{5} - \frac{8}{5} \right) \]
Subtract the fractions: \[ \frac{2}{5} - \frac{8}{5} = \frac{2 - 8}{5} = \frac{-6}{5} \]
Now multiply by 15: \[ 15 \left( \frac{-6}{5} \right) = 15 \cdot \frac{-6}{5} = \frac{15 \cdot -6}{5} = \frac{-90}{5} = -18 \]
Therefore, the final result is: \[ \boxed{-18} \]