Cannot copy text from InDesign CS6

Try trashing your InDesign Preferences:

Close and relaunch InDesign, and IMMEDIATELY hold down Ctrl + Alt + Shift (Windows) or Cmd + Ctrl + Opt + Shift (Mac), and respond in the affirmative to the dialog asking if you really want to replace the preferences. You must be extremely fast on the keyboard (if you don’t see the confirmation prompt, you were too slow!)

You may need to do it a couple of times before you get the hang of it!

Try this, uninstall InDesign using the drop down in the Creative Cloud app (see below screen shot), run Adobe Cleaner Use the Creative Cloud Cleaner Tool to solve installation problems

and then reinstall InDesign

(Having stated all that, maybe your version of CS6 is not the cloud version)

Did you check your Clipboard prefs? Anything odd going on in there?

Also there is a more extensive reset detailed here, that goes beyond the basic reset via modifier keys when starting the software:
Troubleshooting 101: Replace, or "trash" your InDesign preferences

Finally, reboot the computer with no other apps open. Sometimes other applications mysteriously interfere with Adobe apps (browsers and browser extensions in particular, but a number of other apps have been cited to create conflicts as well).