1. **State the problem:** We want to find which expressions are equivalent to $$-4(3d-2)-7$$. 2. **Apply the distributive property:** Multiply $$-4$$ by each term inside the parentheses: $$-4(3d-2) = -4 \times 3d + (-4) \times (-2) = -12d + 8$$ 3. **Combine like terms:** Now subtract 7: $$-12d + 8 - 7 = -12d + (8 - 7) = -12d + 1$$ 4. **Compare with given options:** - Option A: $$-12d - 15$$ (not equal to $$-12d + 1$$) - Option B: $$12d - 15$$ (not equal to $$-12d + 1$$) - Option C: None of the above (correct because neither A nor B matches) **Final answer:** Only option C is correct because the simplified expression is $$-12d + 1$$, which does not match A or B.