1. Do I need to purchase 2 licenses for my computers in different platform? One is desktop in windows, another is macbook pro.
2. Is it possible for me to install cs6 on more than one computer by using one license?
If you buy the perpeptual license then it would be OS specific , in that case you would have to buy 2 seperate license however If you go for the Creative Cloud then in that case it would be OS independent , you can install with creative cloud on 2 Windows or 2 Mac or 1 windows and 1 Mac.
Also , with each license you get 2 activation hence 2 can use the software on 2 machine but not at the same time.