How to find state tax liability on a 1040

you need to tell us what state or look on the form for a line that might say "income tax" or "tax liability" or even something else. 

arizona state tax liability, 

Your tax liability is any amount you owe a taxing authority, such as the IRS or the state where you live or work. Your 2019 AZ state Tax liability is reported on line 52 on Form 140. Your Federal Tax liability is reported on form 1040 line 16.

Can anyone tell me where I would find this for the state of North Carolina?

On North Carolina Form D-400 for 2022, your net income tax liability after credits is on Line 17.

The lines that follow account for consumer use tax, withholding, other payments, penalties, and interest.

The amount due with the return is on Line 27.