1. **State the problem:** Simplify the expression $4x - (3x+2)(4x-1)$. 2. **Use the distributive property:** Expand the product $(3x+2)(4x-1)$ using the FOIL method: $$ (3x+2)(4x-1) = 3x \cdot 4x + 3x \cdot (-1) + 2 \cdot 4x + 2 \cdot (-1) $$ 3. **Calculate each term:** $$ 3x \cdot 4x = 12x^2 $$ $$ 3x \cdot (-1) = -3x $$ $$ 2 \cdot 4x = 8x $$ $$ 2 \cdot (-1) = -2 $$ 4. **Combine the terms:** $$ 12x^2 - 3x + 8x - 2 = 12x^2 + 5x - 2 $$ 5. **Substitute back into the original expression:** $$ 4x - (12x^2 + 5x - 2) $$ 6. **Distribute the negative sign:** $$ 4x - 12x^2 - 5x + 2 $$ 7. **Combine like terms:** $$ (4x - 5x) - 12x^2 + 2 = -x - 12x^2 + 2 $$ 8. **Rewrite in standard polynomial form:** $$ -12x^2 - x + 2 $$ **Final answer:** $$\boxed{-12x^2 - x + 2}$$