Mac OS X 10.6 is no longer supported. Not sure why you're getting prompted to update. If you need Flash Player you can go to System Preferences > Flash Player > Updates tab and toggle the update check to 'never check for updates'.
If you don't need Flash (Adobe will be end-of-lifing it at the end of the year and all browsers will stop supporting it at that time), you can just uninstall it. See https://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html to download the uninstaller.