uninstall (using the uninstallers) everything cc including the desktop app and clean per Use the Adobe Creative Cloud Cleaner Tool to solve installation problems
restart your computer and open a cs6 app. if given the option click to license or purchase and enter your serial number when prompted.
In this case , you can try clearing SLCache contents first instead of starting with Un-installation process right away .
This will erase corrupt or outdated license files.
Enable Hidden files and folder view , because most of files inside SLCache will be hidden by deafult.
All Adobe apps will ask to re-enter serial number once you clear SLCache contents.
Navigate to C : > Program Files ( x86) . Common Files > Adobe .
Under Common Files > Adobe , locate SLCache folder and move all it contents on to a backup fodler on Desktop.
Make sure it is empty .
Then launch CS 6 app and try to Sign in.
Still same ??
Also try Signing in with different Adobe ID and check.
Let me know if you had purchased and activated Creative Cloud subscription previously??
For Mac :
SLCache location : /Library/Application Support/ Adobe.
If you had already tried , still even though you are performing uninstall and re installation process , it will be ideal to clear SLCache contents.