On form 4868 (automatic extension form), Line 7 asks "Amount you're paying". I already entered 8K for my estimated tax liability for 2020. what do I put?

you are expected to  pay something with Form 4868, since you are asking for extension of time to file but not more time to pay what you owe.

If you know you are getting a refund, you will not need an extension.

OR

put zero, you can submit the Form that way.

P.S. the time to request extension is long past so IRS will deny your form 4868.

You only had until May 17 to request an extension for your 2020 tax return.  So you cannot file that 4868 now; it will not do you any good at all.    Even if you are a winter storm victim in TX, you had to mail the 4868 by June 15, so it is just too late.    If you are getting a tax refund there is no penalty for filing late.   If you owe tax due for 2020, now you are just late and you will be subject to late penalties and interest on the tax owed.   This will not be calculated by TurboTax.  The IRS will calculate those amounts and bill you after they receive your return and your payment for the tax due as shown on your Form 1040.