Dreamweaver

you'll need to (carefully) deactivate on your old computer in order to allow activation on your new computer.

that old computer will, at least, need os and default browser security updates to convey the deactivation to adobe's servers.  messing that up is very easy to do and will disable cs6 on the old computer and prevent activation on any other computer. ie, if you can still use the old computer and its cs6, you should probably leave well-enough alone.

Its Adobe Creative Suite 6

is that a subscription version or cs6, 5.5 or 5 or something older?