1. **State the problem:** Expand and simplify the expression $$(3x + 2)(x - 4)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (3x + 2)(x - 4) = 3x \cdot x + 3x \cdot (-4) + 2 \cdot x + 2 \cdot (-4) $$ 4. **Calculate each term:** $$ = 3x^2 - 12x + 2x - 8 $$ 5. **Combine like terms:** $$ = 3x^2 + \cancel{-12x + 2x} + (-8) = 3x^2 - 10x - 8 $$ 6. **Final answer:** $$ 3x^2 - 10x - 8 $$ This is the expanded and simplified form of the given expression.