It depends. However, if I was to guess, then state B is likely NJ, PA or MA. All three of these states will double-up income that is also reported to another state (usually NY), but there is a way to remove the income. The Massachusetts interview asks a specific question regarding this income and is easily removed.
If state B is NJ, you will see a screen in the NJ return entitled About these wages. You will need to make sure the box is checked to exclude State A's income being reported from the NJ return.
If State B is PA, you will see a screen in the PA interview entitled Confirm these wages. This will also have a checkbox that toggles to make the State A-reported income not taxable/taxable in PA. Make sure State A is marked as Not Taxable in PA.
If State B is another state, please comments so we can further assist you (and commenting State A might also be helpful).
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