Bluetick1010

beatthecfa has already posted a complete answer. I will just try to add a conceptual note.

Always have this fundamental equation in mind
A = L + E

1) Your Asset (A) has decreased by $20.

2) Means right side of your equation (L or E or both) MUST decrease in value, in order to balance it. (or you increase some other Asset, which is not the case here)

3) Now, Equity (E) gets affected thru Net Income mostly. (There are cases when Equity can be affected directly, but this is not one of them). And Net Income you get is AFTER the Tax Effect. So, in this case, decrease in your Equity (E) can only be upto ($20 x .65) = $13

4) You now have only reduced the left side by $13. And remaining $7 can only be reduced from Liability (cannot reduce from E any more amount).

5) And the remaining $7 is reduced from L as 'tax liability'. 'Deferred tax liability' in this case.

Last step (5) would be answer to your question "Why do they adjust liabilities by the after-tax value?".