How is it that you don’t have the disks or the serial number? You can’t do anything without the serial number at all.
You can log into your account to get it as long as you registered.
You can download CS6 installers from here: https://helpx.adobe.com/x-productkb/policy-pricing/cs6-product-downloads.html
Note that if you’re running El Capitan, you are on your own. Lots of reported issues and CS6 has reached end of life and will receive no further updates.
The disks were installed by a previous employee, and the technology department can't locate the information so I'm in need of an alternate solution if once exists. I'm using OS Mavericks, and I've deleted the preferences but to no avail!
If you know the identity used to register the program you can retrieve the serial number from the account at Adobe.com for that identity.
I gave you the link for the installers but I can't help with serial number. You need to check the account at Adobe.com but as Peter points out, you need to know the Adobe ID that was used.
I don't a perpetual version installed so I can't even check to see if you can find that anywhere.