1. **State the problem:** Solve the linear equation $$-4(m + 10) = 8m + 4(-12 - 2m)$$ for the variable $m$. 2. **Apply the distributive property:** Multiply the constants outside the parentheses by each term inside. $$-4(m + 10) = -4 \times m + -4 \times 10 = -4m - 40$$ $$4(-12 - 2m) = 4 \times -12 + 4 \times -2m = -48 - 8m$$ So the equation becomes: $$-4m - 40 = 8m - 48 - 8m$$ 3. **Simplify the right side:** Combine like terms. $$8m - 8m = 0$$ So the equation is: $$-4m - 40 = -48$$ 4. **Isolate the variable term:** Add 40 to both sides. $$-4m - 40 + 40 = -48 + 40$$ $$-4m = -8$$ 5. **Solve for $m$ by dividing both sides by $-4$:** $$m = \frac{-8}{\cancel{-4}} \times \frac{\cancel{-1}}{1} = 2$$ 6. **Final answer:** $$\boxed{m = 2}$$