Is Adobe CS6 compatible with Sonoma?

Adobe discontinued the one-time purchase versions of Photoshop and Lightroom some time ago – and, as I recall, never updated the installation and activation code of the one-time versions to work on newer versions of macOS.

You might want to take a look at the Adobe Photography Plans. Those are "subscription" (rental) plans. Some of them include access not just to the cloud-oriented version of Lightroom, but to Lightroom Classic and Photoshop.

https://www.adobe.com/creativecloud/photography.html

If you're not tied to Adobe applications, specifically, there are the Affinity V2 programs (Photo, Designer, Publisher), which are available for a one-time purchase fee.

https://affinity.serif.com/en-us/

You can't use CS6 on newer MAC OS. Apple discontinued supporting 32 bit applications since Catalina and CS6 has some 32 bit components in it so it's a no go. But you can use Illustrator.