It depends. The question is asking how much of the income that is being reported to Illinois was actually earned in another state, in this case NY, so that the credit for taxes to another state may be calculated correctly. For this question, if the amount reported to NY is taxable to NY, this is the information you will put in this box.
However, there are other factors. NY has some tricky laws when it comes to income that is taxable to NY. Although you did not live there, you are considered as working in NY if you worked remotely from home. In this circumstance, (which seems to be the case here) you file a NY nonresident return on all of your income, and both Illinois and NJ will give you credit for the NY income that you earned while in each state, since each taxes the amount of income you earned in NY during the same time period.
If, however, NY was not supposed to tax this income, you still file the NY nonresident return, but you will allocate the income in New York. Your Illinois income would not be taxable in NY if you were working in an Illinois office instead of from home, and you would want to indicate that this income is not taxable.
Either way, you do wish to prepare the nonresident return first to get accurate calculations. Here's an FAQ to assist you with this: https://ttlc.intuit.com/replies/3302052
[edited 3/5 2017 6:03 PST]
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