1. **State the problem:** Solve the equation $-8(x-3)+4=4(-x+8)-4x$ for $x$. 2. **Apply the distributive property:** $$-8(x-3) = -8x + 24$$ $$4(-x+8) = -4x + 32$$ So the equation becomes: $$-8x + 24 + 4 = -4x + 32 - 4x$$ 3. **Simplify both sides:** Left side: $-8x + 24 + 4 = -8x + 28$ Right side: $-4x + 32 - 4x = -8x + 32$ So the equation is: $$-8x + 28 = -8x + 32$$ 4. **Add $8x$ to both sides to eliminate $x$ terms on the left:** $$\cancel{-8x} + 28 + 8x = \cancel{-8x} + 32 + 8x$$ Simplifies to: $$28 = 32$$ 5. **Analyze the result:** Since $28 \neq 32$, this is a contradiction. 6. **Conclusion:** The equation has no solution because it leads to a false statement. **Final answer:** No solution.