Dear Student,
Old goodwill is the goodwill that appears in the Balance Sheet (Old Balance Sheet). This goodwill is to be debited (as it is being written-off) to the partners' capital accounts in their old profit sharing ratio.
Compensated goodwill is the one given to you in the adjustments (or as additional information beneath the Old Balance Sheet). This goodwill is to be adjusted by debiting the gaining partners and crediting the sacrificing partners. This is the compensation that gaining partners (who receive more share in future profits) make to sacrifice partners (who receive lesser share in future profits).