DVD OR CD?

What OS and version of that OS are you running?

There's a good chance that older CS versions might not work with an up-to-date OS.

The only ways I think Adobe Illustrator CS6 would have been released on different media types (CD or DVD) is if it was either sold as a stand-alone retail product or if it was packaged as part of a larger Creative Suite package. The Master Collection retail box had the application installers stored on DVD-ROM discs. A Creative Suite box with fewer applications, such as CS6 Design Premium or CS6 Design Standard may have had multiple CD-R discs. An individual retail box of Illustrator CS6 may have had only one or two CD-R discs. That's a step up from an Illustrator installer on floppy discs.

Either way, I don't think there was any difference in terms of extra "goodies" that were included with an Illustrator CS6 installer on CD or DVD. I remember being disappointed by the lack of bonus content (like hardly any fonts) in the CS5.5 Master Collection box. I sure don't have any complaints about lack of fonts when it comes to Creative Cloud.

I think at the time it was just a choice of how someone could load it onto their computer.

version CS6 was 12 years ago. WHat is the reason you are asking about it?