How can I make this BS balance? (Intercorporate Investments)

CFA Level II FRA
#1

As pictured, imagine Company P acquires 80% of Company S for $8,000 cash to shareholders.

In order to introduce goodwill to the mix, I have said that the fair value of S’ equity value at time of acquisition is $12,000. I just can’t work out what I need to change to make this balance?

Screenshot 2022-11-23 081332
Screenshot 2022-11-23 0813321091×614 20.5 KB

Any help much appreciated.

#2

So, if fair value of 100% of the company is $12000, $9600 would be the fair value of the 80%. If you pay 8000 for 80% of the company, you should recognize a gain of $9600-$8000= $1600 in your income statement, which will add up to $98000 equity, which will balance your BS statement.

I am not sure though