1. Start by stating the problem: Simplify and expand the expression $$-2x^2 + 9x - 4 - (-2 - x)(3x - 12)$$. 2. Expand the product $$(-2 - x)(3x - 12)$$ using the distributive property: $$-2 \times 3x = -6x$$ $$-2 \times (-12) = +24$$ $$-x \times 3x = -3x^2$$ $$-x \times (-12) = +12x$$ 3. Combine these to get: $$-6x + 24 - 3x^2 + 12x$$ 4. Now, substitute back into the original expression, remembering the minus in front: $$-2x^2 + 9x - 4 - ( -6x + 24 - 3x^2 + 12x )$$ 5. Distribute the minus sign over the parentheses: $$-2x^2 + 9x - 4 + 6x - 24 + 3x^2 - 12x$$ 6. Combine like terms: For $$x^2$$ terms: $$-2x^2 + 3x^2 = x^2$$ For $$x$$ terms: $$9x + 6x - 12x = 3x$$ Constants: $$-4 - 24 = -28$$ 7. The simplified expression is: $$x^2 + 3x - 28$$ Final answer: $$\boxed{x^2 + 3x - 28}$$