Do you actually own the CS6 which came with your second hand computer? Is it registered under your Adobe ID in your Adobe account?
Was the software license transferred to your name via the official Adobe process?
It was not, but I am still in contact with the guy I bought it from.
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The first thing to do is get the ownership of the software license in order - if Adobe still administers license transfers. Adobe is so focussed on their Cloud products that their resources for dealing with such ancient software licenses are fast disappearing.
Reinstalling the software on a different computer is then trivial. You cannot "transfer" Adobe software - it must be reinstalled from scratch.
Download the installer from Download Adobe Creative Suite 6 applications , install then enter your serial number.