1. **State the problem:** Simplify the expression $$-0.3(-2d - 5f) + 4f - 0.3(-f + 7d)$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. This means we multiply each term inside the parentheses by the factor outside. 3. **Apply distribution:** $$-0.3(-2d) + -0.3(-5f) + 4f + -0.3(-f) + -0.3(7d)$$ 4. **Calculate each multiplication:** $$0.6d + 1.5f + 4f + 0.3f - 2.1d$$ 5. **Combine like terms:** Group the $$d$$ terms: $$0.6d - 2.1d = \cancel{0.6d} - \cancel{2.1d} = -1.5d$$ Group the $$f$$ terms: $$1.5f + 4f + 0.3f = 5.8f$$ 6. **Write the simplified expression:** $$-1.5d + 5.8f$$ **Final answer:** $$\boxed{-1.5d + 5.8f}$$