1. **State the problem:** Solve the equation $2(4x+3)+4=-2(-4x-6)-2$ for $x$. 2. **Apply the distributive property:** Multiply out the parentheses. $$2 \times 4x + 2 \times 3 + 4 = -2 \times (-4x) - 2 \times (-6) - 2$$ which simplifies to $$8x + 6 + 4 = 8x + 12 - 2$$ 3. **Combine like terms on each side:** Left side: $6 + 4 = 10$ Right side: $12 - 2 = 10$ So the equation becomes $$8x + 10 = 8x + 10$$ 4. **Subtract $8x$ from both sides:** $$\cancel{8x} + 10 = \cancel{8x} + 10$$ which simplifies to $$10 = 10$$ 5. **Interpret the result:** Since the equation reduces to a true statement $10=10$ with no variables left, this means the original equation is true for all values of $x$. **Final answer:** The solution is all real numbers, or $x \in \mathbb{R}$.