Need someone to explain the adoption tax credit

I thought I had it figured out, but recently read something that confused me all over again. Here is a scenario. If someone who understands the credit can read my scenario and explain what would happen I would be very appreciative. Example: DH and I owe $9,000 in taxes for the year We paid $10,000 in taxes for the year The adoption tax credit is $12,000 Assume that we will qualify to the entire credit based on income and adoption expenses. How will this work for us? In this scenario, I think that we will only get the $9,000 back in addition to the $1,000 we would get back anyway right? If this is the case, can we get the other $3,000 back the next year? I am so confused and the IRS site did nothing to help me. Thanks!