The way it works is this:
If you have to pay income taxes to a different state and DE is your home state of residence, then you complete the other state tax return and determine the amount of tax liability to the other state as a nonresident on the income earned in the other state and taxed by DE (since you are a DE resident, all income earned everywhere is taxable to a DE resident).
Once you have determined the tax liability due to the other state on the income also taxed by DE, you go to the DE return "other state tax credit worksheet" and enter the other state's tax liability and the other state's income also taxed by DE and you get an other state tax credit to claim on your DE return.
For additional information, please refer to the following link:
DE Instructions for other state tax credit
