$$\frac{8}{15} \cdot \frac{25}{32} = \frac{8 \cdot 25}{15 \cdot 32} = \frac{200}{480} $$.
Сократим дробь на 40.
$$\frac{200}{480} = \frac{200:40}{480:40} = \frac{5}{12} $$.
Ответ: $$\frac{5}{12}$$