1. **State the problem:** Simplify the expression $4(3x - y)$. 2. **Formula used:** Use the distributive property of multiplication over subtraction: $$a(b - c) = ab - ac$$ 3. **Apply the distributive property:** Multiply 4 by each term inside the parentheses: $$4 \times 3x = 12x$$ $$4 \times (-y) = -4y$$ 4. **Combine the results:** $$4(3x - y) = 12x - 4y$$ 5. **Conclusion:** The simplified expression is $12x - 4y$, which corresponds to option C.