1. **State the problem:** Solve the equation $$\frac{2}{3}x = 8$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the reciprocal of the fraction coefficient. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. 3. **Multiply both sides by the reciprocal:** $$\frac{3}{2} \times \frac{2}{3} x = 8 \times \frac{3}{2}$$ 4. **Cancel common factors:** $$\cancel{\frac{3}{2}} \times \cancel{\frac{2}{3}} x = 8 \times \frac{3}{2}$$ 5. **Simplify:** $$x = 8 \times \frac{3}{2}$$ 6. **Calculate the right side:** $$x = \frac{8 \times 3}{2} = \frac{24}{2} = 12$$ **Final answer:** $$x = 12$$