1. **State the problem:** We need to subtract the polynomial $$(-5x^6 + 4x^4 + 2x)$$ from $$8x^6 - 10x^4 - 3x$$. 2. **Write the expression:** $$ (8x^6 - 10x^4 - 3x) - (-5x^6 + 4x^4 + 2x) $$ 3. **Apply the subtraction:** Subtracting a polynomial means changing the signs of each term in the second polynomial and then adding: $$ 8x^6 - 10x^4 - 3x + 5x^6 - 4x^4 - 2x $$ 4. **Combine like terms:** - Combine the $$x^6$$ terms: $$8x^6 + 5x^6 = 13x^6$$ - Combine the $$x^4$$ terms: $$-10x^4 - 4x^4 = -14x^4$$ - Combine the $$x$$ terms: $$-3x - 2x = -5x$$ 5. **Final answer:** $$ 13x^6 - 14x^4 - 5x $$ This is the simplified result after subtraction.