here the question is "calculate the hidden goodwill of the firm?"
Ans; goodwill means the value of the firm which is generated due to continuous opertions of the firm. the goodwill is generated by the existing partners and not the new incoming partner.
therefore the incoming partner capital amount must contain a portion for goodwill but the existing partners amount does not contain a portion for goodwill
therefore the actual capital of the firm with goodwill must be
12000------------1/4
? ------------3/4
12000 * 3/4/1*4
total capital with goodwill=36000+12000=48000
but the capital of a+b+c= 10k+20k+12k=42k therfore hidden goodwill =48k-42k=6000