1. **State the problem:** We want to find which expressions are equivalent to $$4(3j+(-4))-9$$. 2. **Start by simplifying the original expression:** $$4(3j + (-4)) - 9 = 4(3j - 4) - 9$$ 3. **Distribute the 4:** $$= 4 \times 3j - 4 \times 4 - 9 = 12j - 16 - 9$$ 4. **Combine like terms:** $$12j - 16 - 9 = 12j - 25$$ 5. **Check option A:** $$-12j - 13$$ This is not equal to $$12j - 25$$, so option A is not equivalent. 6. **Check option B:** $$-4(-3j + 4) - 9$$ Distribute the -4: $$= -4 \times -3j + (-4) \times 4 - 9 = 12j - 16 - 9$$ Combine like terms: $$= 12j - 25$$ This matches the simplified original expression. 7. **Option C:** "None of the above" is false because option B is equivalent. **Final answer:** Only option B is equivalent to the original expression.