The kicker is the balance transfer fees (not to be confused with the interest rate). My guess is that B charges a flat 2-3% fee upfront just for doing the transfer. The "0% interest" might also be deferred, meaning if you miss a payment (intentionally or from some mistake) or don't pay off the balance in 12 months, they'll retroactively charge you all of the interest that had been accruing but you hadn't been charged. All that should be outlined in the terms of the transfer agreement. Read it very carefully.
So, can you do this? Sure - it will cost you 9% over 2 years (3% for each transfer plus 3% for the second year after you transfer back), and after two years you'll still be in debt. You haven't really accomplished anything, just moved your debt around for a slightly lower interest rate. Plus if something happens and you can't pay the monthly payment, you might end up MUCH worse off than when you started.
Depending on how long you plan to take to pay this off, you might be better off, but if it only takes you 6 months to get it paid off, you might be better off paying the higher interest instead of the 3% upfront fee and the risk of extra fees if something goes wrong.