1. **State the problem:** Solve the equation $$3(4 - x) = 6(x + 2)$$ for $x$. 2. **Rewrite the equation:** Distribute the constants on both sides: $$3 \times 4 - 3 \times x = 6 \times x + 6 \times 2$$ which simplifies to $$12 - 3x = 6x + 12$$ 3. **Bring all terms involving $x$ to one side and constants to the other:** $$12 - 3x - 6x = 12$$ $$12 - 9x = 12$$ 4. **Subtract 12 from both sides:** $$\cancel{12} - 9x = \cancel{12}$$ $$-9x = 0$$ 5. **Divide both sides by $-9$ to isolate $x$:** $$x = \frac{0}{-9}$$ $$x = 0$$ 6. **Final answer:** $$\boxed{0}$$