Can't tell the difference- tax paid by recipient vs tax paid by gifter

Ok, so I just got a problem that asked to find the relative value of a lifetime gift, assuming that the girt tax is paid by the recipient. So, essentially you just use that gift tax as the estate tax in the numerator to find the relative value.

But, what if the problem said “assuming that the gift tax is paid for by the gifter?”

How would you go about that? Would it add back the deduction to the FV of the gift value at the end of the numerator?

Very confused on this, would appreciate some guidance.