You have a bit of a tricky situation to calculate, and I might need a few more details. The idea behind the "double-taxed income" window is to determine the income that was taxed BOTH by New York and New Jersey at the same time. In your case, it will be the income you earned in New York while living in New Jersey. By the way you worded your response, that would be any income you worked in the last 5 months of the year. Unemployment does not count, because while New York does tax unemployment compensation, New Jersey does not. So if you received New York-sourced unemployment after moving to New Jersey, you will continue to pay NY tax on that income, but that income will not qualify for a New Jersey tax credit.
Make sure you have prepared your New York return first to get the amount of income and tax you are claiming and is being taxed by New York. Once you have the gross amounts being taxed by New York, then you need to figure out how much you are taxed. To figure this out, add up the New York tax withheld from your Forms W-2 and 1099-G (unemployment). Next, subtract any refund you are receiving from New York. If instead you owe New York, then add the amount you owe. This number represents New York's tax on New York income.
Now, to find out how much of this income is double-taxed, you need to figure out how much has been reported also to New Jersey. That number could be on your W-2 (which would make your life a lot easier if it is). If it is not, then you will probably need to do some math. Take the W-2 that has the double-taxed income, and multiply that amount by the percentage of income earned while living in New Jersey. (If I read your information correctly, you worked this particular job for 7 months total, but 5 while living in New Jersey. If that is correct, then the double-taxed income would be 5/7 of the total income, or roughly 71.4% That number represents the double-taxed income.
Next, you need to figure out your percentage of double-taxed income on your New York return. Divide the New Jersey double-taxed income you figured out in the above paragraph by your total New York income (including unemployment). That produces a percentage. Now, multiply that percentage by (1) the total New York income (and that should give you the same number as the paragraph above. This number you can put in Box 1 of your screenshot: Double-taxed income while a resident of New Jersey. Now, use that same percentage and multiply by the amount of net New York Tax, which is the amount you figured out in the second paragraph. This prorate is New York's tax on the double-taxed income.
New Jersey's credit will be the lower of what New Jersey taxes the double-taxed income or what New York taxes the double-taxed income. Also, make sure that when you are in the New Jersey return, you have reviewed the screen About this W2 income. On that screen, you must be sure to check the NY box to make sure that the NY income is not being double-added on your New Jersey return, thus making your NJ income (and tax) even higher than what it should be.
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