Example of the Credit for Taxes Paid to Another State
Let's say you live in New Jersey but you commute to New York for work. New Jersey taxes all of your income because you are a full-year resident. New York taxes your wages because you earned them in New York. So your wages are being taxed by both New Jersey and New York.
New Jersey would allow a credit for the taxes you paid to New York so that you aren't being taxed by two states on the same income. The credit would be limited to the smaller of the amount of tax you actually paid to New York, or the amount of tax New Jersey would charge for that same income.
You would need to look at your completed New York tax return to determine your income that was taxable in New York and your actual tax liability to New York. You would use those numbers to calculate the Credit for Taxes Paid to Another State for New Jersey.