1. **State the problem:** Solve the equation $$12 - 8 = \frac{2}{3}x - 4$$ for $x$. 2. **Simplify the left side:** $$12 - 8 = 4$$ So the equation becomes: $$4 = \frac{2}{3}x - 4$$ 3. **Isolate the term with $x$:** Add 4 to both sides: $$4 + 4 = \frac{2}{3}x - 4 + 4$$ $$8 = \frac{2}{3}x$$ 4. **Solve for $x$:** Multiply both sides by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$: $$x = 8 \times \frac{3}{2}$$ 5. **Calculate the product:** $$x = \cancel{8} \times \frac{3}{2} = 4 \times 3 = 12$$ **Final answer:** $$x = 12$$