Here is how the state credit works

A state resident receives $20,000 from a rental building in B. The resident reports only the $20,000 to B and pays $2,000 in tax to B. Since the person is a A resident, A also taxes the $20,000, but gives a $2,000 tax credit for the tax you paid to B. For example, if A state rate is 15%, you need pay $1,000 to A state besides the $2,000 you already paid to B state.