CS 6 is not offered through the Creative Cloud desktop app. You can download any or all of the CS6 applications from the Adobe download site. Then install them using your serial number.
But I think if you have the full suite you need a special download that includes all of the programs. As far as I know the full suite comes with only one license serial number and doesn't work with individual installs of the programs. That is just an assumption as I have never used the full suite of programs.