1. **State the problem:** Simplify the expression $-4(8f + g) + 9g - 5(-2g + 6f)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$-4(8f + g) = -4 \times 8f + (-4) \times g = -32f - 4g$$ $$-5(-2g + 6f) = -5 \times (-2g) + (-5) \times 6f = 10g - 30f$$ 3. **Rewrite the expression with distributed terms:** $$-32f - 4g + 9g + 10g - 30f$$ 4. **Combine like terms:** Group $f$ terms and $g$ terms separately. $$(-32f - 30f) + (-4g + 9g + 10g)$$ 5. **Simplify each group:** $$-32f - 30f = -62f$$ $$-4g + 9g + 10g = 15g$$ 6. **Final simplified expression:** $$\boxed{-62f + 15g}$$