1. **State the problem:** Simplify the expression $$- \frac{3}{4}(10m + 8) - \frac{1}{2}(21m - 16)$$. 2. **Apply distributive property:** Multiply each term inside the parentheses by the coefficients outside. $$- \frac{3}{4} \times 10m = - \frac{30}{4}m = - \frac{15}{2}m$$ $$- \frac{3}{4} \times 8 = -6$$ $$- \frac{1}{2} \times 21m = - \frac{21}{2}m$$ $$- \frac{1}{2} \times (-16) = +8$$ 3. **Rewrite the expression:** $$- \frac{15}{2}m - 6 - \frac{21}{2}m + 8$$ 4. **Combine like terms:** Combine the $m$ terms: $$- \frac{15}{2}m - \frac{21}{2}m = - \frac{36}{2}m = -18m$$ Combine the constants: $$-6 + 8 = 2$$ 5. **Final simplified expression:** $$-18m + 2$$ **Answer:** The simplified form of the expression is $$\boxed{-18m + 2}$$.