Adobe allows you to install the same purchased serial number on no more of two of your computers.
If you buy the box packaging from an authorized reseller, you can get two installation discs, one for Windows and one for Mac.
If you purchase an online download, then you get a version specific to the computer operating system to which it is downloaded.
Also, it has been written here many times that you are supposed to use the two one at a time.
Just be sure that what you purchased is supported by the computer operating system involved.
Any questions or need clarification, please do not hesitate to ask.