Activating my application [serial number is already in use]

Try the offline activation as described as Solution 2 in the linked document.

https://helpx.adobe.com/creative-suite/kb/serial-number-validation-launching-cs6.html

But be aware: if you have reached your activation limit and you don't have any chance to deactivate an older installation you're out of luck. Adobe has stopped the support of CS 6 products and the resetting of the activation counter isn't possible anymore.

@VJM1952 CS6 for Windows 11? So, there are a few issues here. CS6 is from a long time ago, like 2012 (heck, I don't think Windows 8 was out yet!!)—Adobe "retired" the activation servers for CS6. Even if you have a valid case number, their customer support agents generally no longer have the tools to manually "reset" a CS6 serial number because those 'servers are gone' — plus, by using old software, you could be more susceptible to security threats! 

You could try this; disconnect your internet before running the installer. Sometimes, choosing "Install as Trial" allows you to get the software onto the disk. Once installed, reconnect and try to enter the serial.

But here is a post for legacy apps: https://helpx.adobe.com/download-install/apps/troubleshoot/licensing-activation-issues/cant-activate-reinstall-legacy-apps.html

Good Luck!