On your W-2, if state taxes were withheld for both PA and DE, make sure that both are entered in lines 15-17. You can do this by selecting Add another state.
After doing that, you want to prepare your nonresident PA return before your DE return. In the Compensation Summary screen, you want to make sure that only your PA wages are being taxed by PA. You should see your employer with PA as the state ID. Click edit and make sure the amount is the same as what is being reported taxable by PA in Box 16 of your W-2. If there are other employers, make sure that none of their income is taxable in PA. If you have any other forms of income, make sure none of them are being taxed by PA.
PA usually withholds the exact right amount of taxes since they do not offer many credits and they have a flat tax rate. If you are owing them a lot of money or they owe you a lot of money, chances are something is entered incorrectly.
Once you complete the PA return, the credit for the taxes you pay to them will automatically be applied to your DE return. This will lower the amount of taxes you owe on the same income. Since DE is your resident state, all of your income is taxable there, both your compensation from this job as well as any other forms of income you have.
You may owe DE additional money if the credit you received from PA and the additional DE taxes they withheld were not enough to cover the taxes you owe to DE. You might owe additional money depending on if your employer is correctly withholding taxes based on your situation and if you have other forms of income besides your job.
