1. **State the problem:** We need to simplify or find the result of the expression combining the two polynomials: $$4x^3 + 8x^2 - 4x + 4$$ and $$4x^3 - 8x^2 - x - 8$$. 2. **Add the polynomials:** Combine like terms by adding coefficients of the same powers of $x$: $$\begin{aligned} &(4x^3 + 8x^2 - 4x + 4) + (4x^3 - 8x^2 - x - 8) \\ &= (4x^3 + 4x^3) + (8x^2 - 8x^2) + (-4x - x) + (4 - 8) \\ &= 8x^3 + 0x^2 - 5x - 4 \end{aligned}$$ 3. **Simplify the expression:** $$8x^3 - 5x - 4$$ 4. **Final answer:** The sum of the two polynomials is $$8x^3 - 5x - 4$$.