1. **State the problem:** Solve for $u$ in the equation $$-\frac{4}{5}u = -12$$. 2. **Recall the multiplicative property of equality:** To isolate $u$, multiply both sides of the equation by the reciprocal of the coefficient of $u$. 3. The coefficient of $u$ is $-\frac{4}{5}$. Its reciprocal is $-\frac{5}{4}$. 4. Multiply both sides by $-\frac{5}{4}$: $$\left(-\frac{5}{4}\right) \times \left(-\frac{4}{5}u\right) = \left(-\frac{5}{4}\right) \times (-12)$$ 5. Simplify the left side by canceling common factors: $$\cancel{-\frac{5}{4}} \times \cancel{-\frac{4}{5}} u = \frac{5}{4} \times 12$$ 6. The left side simplifies to $u$ because the product of a number and its reciprocal is 1. 7. Calculate the right side: $$u = \frac{5}{4} \times 12 = \frac{5 \times 12}{4} = \frac{60}{4}$$ 8. Simplify the fraction: $$u = 15$$ **Final answer:** $$u = 15$$