1. **Problem:** Simplify the expression $-\frac{9}{5} \cdot \frac{8}{15}$. 2. **Formula:** To multiply fractions, multiply the numerators and multiply the denominators: $$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$$ 3. **Apply the formula:** $$-\frac{9}{5} \cdot \frac{8}{15} = \frac{-9 \cdot 8}{5 \cdot 15} = \frac{-72}{75}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 72 and 75, which is 3. 5. **Divide numerator and denominator by 3:** $$\frac{\cancel{72}^{{24}}}{\cancel{75}^{{25}}} = \frac{-24}{25}$$ 6. **Final answer:** $$-\frac{24}{25}$$ This means the product of $-\frac{9}{5}$ and $\frac{8}{15}$ simplifies to $-\frac{24}{25}$.