They will not accept them just from your first college’s transcript. You will need to have official score reports sent to the new college. After the scores are received, they will be evaluated and recorded according to that institution’s policy. Often transfer credits and credits by exam are not finalized until after a student is on campus so you have plenty of time to sort this out.
If the new college can only accept 60 credits total of the 68 that you have, make sure that they transfer the ones that are the most useful for your degree program, and find out if any of the extra ones can qualify to place you into higher level courses that you want to take.