How do I determine the amount that I should put in the taxpayer's column (right column) for the question "Tax Due to NY on income above" for form PA Schedule G-L?

You need to look at the NY form. Since you are using the online version:

1. Open the NY return
2. Select the dropdown arrow next to Tax Tools. 
3. Select Tools, then 
4. Select View Summary.
5. Verify your summary shows NY at the top or you will need to select it from the left side. 
6. Look for the taxable income and liability. 
7. Make a note of the numbers
8. Select back on the left side
9. Return to PA return
10. Enter the tax liability into the PA when asked.

We make up a lot of fake returns to help our customer so all customer things here are fictional.

So, are you saying that I should put the same amount in both the NY column and the Taxpayer's column?  I had already put the tax liability in the NY column.