1. **State the problem:** Multiply the binomials $ (3x - 4)(4x + 3) $ and simplify the result. 2. **Recall the formula:** To multiply two binomials, use the distributive property (FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (3x - 4)(4x + 3) = 3x \cdot 4x + 3x \cdot 3 - 4 \cdot 4x - 4 \cdot 3 $$ 4. **Calculate each term:** $$ 3x \cdot 4x = 12x^2 $$ $$ 3x \cdot 3 = 9x $$ $$ -4 \cdot 4x = -16x $$ $$ -4 \cdot 3 = -12 $$ 5. **Combine like terms:** $$ 12x^2 + 9x - 16x - 12 = 12x^2 - 7x - 12 $$ 6. **Final answer:** $$ \boxed{12x^2 - 7x - 12} $$