1. **State the problem:** Solve the equation $12x - 3(x - 2) = 3(x + 4)$ for $x$. 2. **Apply the distributive property:** Expand the terms with parentheses. $$12x - 3x + 6 = 3x + 12$$ 3. **Combine like terms on the left side:** $$ (12x - 3x) + 6 = 3x + 12$$ $$9x + 6 = 3x + 12$$ 4. **Isolate variable terms on one side:** Subtract $3x$ from both sides. $$9x + 6 - \cancel{3x} = \cancel{3x} + 12 - 3x$$ $$6x + 6 = 12$$ 5. **Isolate the constant term:** Subtract 6 from both sides. $$6x + 6 - 6 = 12 - 6$$ $$6x = 6$$ 6. **Solve for $x$:** Divide both sides by 6. $$\frac{6x}{\cancel{6}} = \frac{6}{\cancel{6}}$$ $$x = 1$$ **Final answer:** $x = 1$