1. **State the problem:** Simplify the expression $-2x^2(4x - x^2 - 3)$. 2. **Use the distributive property:** Multiply $-2x^2$ by each term inside the parentheses. 3. Multiply $-2x^2$ by $4x$: $$-2x^2 \times 4x = -8x^{3}$$ 4. Multiply $-2x^2$ by $-x^2$: $$-2x^2 \times -x^2 = 2x^{4}$$ 5. Multiply $-2x^2$ by $-3$: $$-2x^2 \times -3 = 6x^{2}$$ 6. **Combine all terms:** $$-8x^{3} + 2x^{4} + 6x^{2}$$ 7. **Write the simplified expression in standard polynomial form:** $$2x^{4} - 8x^{3} + 6x^{2}$$ **Final answer:** $$2x^{4} - 8x^{3} + 6x^{2}$$