So I am trying to build a better credit, I have four credit card, one BoA with $2000 and a $0 balance, the other 3 card have a balance total up to $1270. What will happen if I do a balance transfer to my BoA card? can I close the other 3 cards when I do this and what will happen to my credit history and scroe ?
Yes you can Balance Transfer to the BoA card, it may even make sense based on interest rate and the time you will take to pay off the card. No you should not close down your other cards. For best scoring you need 2-3 cards on your Credit Report. If BoA cuts your credit limit for some reason or closes down your account you will be stuck in a bad place. Keep them open untill you get a replacement card with no Anual Fee. After you have 2-3 cards reporting with low or no Anual Fee you can think about closing older cards perferably the new cards should be from diffferent banks or at least not from BoA. At that point shutting down the other cards will only affect your Utilitization rate, they will remain reporting for the next 10 years.
First off, closing cards does not affect your credit history until 10 years after the card is closed (that's when it falls off your report). It will however affect your score though because it will lower your available credit.
What is the reason you want to do the balance transfer? If you aren't paying interest, it makes no sense, as there is a balance transfer fee. I also would not recommend transferring that much (~70% of your BoA credit line) because it would make your Util sky high on that card. That is unless your other three cards are maxed out.
I can help you better if you tell us your credit lines/balances on your other cards as well as interest rates, etc.