1. **State the problem:** Simplify the expression $$3x(x - 2) + 4(3 - 2x^2)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$3x(x - 2) = 3x \cdot x - 3x \cdot 2 = 3x^2 - 6x$$ $$4(3 - 2x^2) = 4 \cdot 3 - 4 \cdot 2x^2 = 12 - 8x^2$$ 3. **Combine the results:** $$3x^2 - 6x + 12 - 8x^2$$ 4. **Group like terms:** $$3x^2 - 8x^2 - 6x + 12$$ 5. **Simplify the coefficients:** $$\cancel{3x^2} - 8x^2 = -5x^2$$ So the expression becomes: $$-5x^2 - 6x + 12$$ 6. **Final answer:** $$\boxed{-5x^2 - 6x + 12}$$