1. **State the problem:** Solve the equation $$-4(2x - 2) = -(4x - 4)$$. 2. **Apply the distributive property:** Multiply $$-4$$ by each term inside the parentheses on the left side. $$-4 \times 2x = -8x$$ $$-4 \times (-2) = +8$$ So the left side becomes $$-8x + 8$$. 3. **Simplify the right side:** The right side is $$-(4x - 4)$$, which means multiply each term inside by $$-1$$. $$-1 \times 4x = -4x$$ $$-1 \times (-4) = +4$$ So the right side becomes $$-4x + 4$$. 4. **Rewrite the equation:** $$-8x + 8 = -4x + 4$$ 5. **Collect like terms:** Add $$8x$$ to both sides to move all $$x$$ terms to the right. $$8 = -4x + 4 + 8x$$ Simplify the right side: $$8 = 4x + 4$$ 6. **Isolate the variable term:** Subtract $$4$$ from both sides. $$8 - 4 = 4x$$ $$4 = 4x$$ 7. **Solve for $$x$$:** Divide both sides by $$4$$. $$x = \frac{4}{4} = 1$$ **Final answer:** $$x = 1$$