1. **State the problem:** Simplify the expression $$-2x(x+3) - (x+1)(x-2)$$ and identify which option matches the result. 2. **Apply distributive property:** $$-2x(x+3) = -2x^2 - 6x$$ $$(x+1)(x-2) = x^2 - 2x + x - 2 = x^2 - x - 2$$ 3. **Rewrite the expression:** $$-2x^2 - 6x - (x^2 - x - 2)$$ 4. **Distribute the minus sign:** $$-2x^2 - 6x - x^2 + x + 2$$ 5. **Combine like terms:** $$(-2x^2 - x^2) + (-6x + x) + 2 = -3x^2 - 5x + 2$$ 6. **Final answer:** $$\boxed{-3x^2 - 5x + 2}$$ which corresponds to option d.