If your copy of PS was for Win, your installation disk is not compatible with Mac. You can't use a Win serial number on Mac either. You would need to contact Adobe Customer Care and request a cross grade. Depending on which version you own, this may no longer be possible. I believe CS6 still qualifies for cross grades though.
Another option is to join the Creative Cloud Photography Plan ($9.99/mo) which includes PS CC and Lightroom which will run on on both Mac & Win.