1. **State the problem:** Solve the equation $32 - 4x = 12x$ for $x$. 2. **Use the formula:** To solve linear equations, we isolate $x$ by moving all $x$ terms to one side and constants to the other. 3. **Step-by-step solution:** $$32 - 4x = 12x$$ Add $4x$ to both sides: $$32 = 12x + 4x$$ $$32 = 16x$$ Divide both sides by $16$: $$\frac{32}{\cancel{16}} = \frac{16x}{\cancel{16}}$$ $$2 = x$$ 4. **Final answer:** $x = 2$