You do need your installers and serial number to reinstall. If you registered the software your serial numbers are available online in your Adobe account for perpetually licensed products (and on the DVD case if you have disks). For CS6 installed through a Cloud subscription, uninstall and reinstall through the CC App. Id you need to download an installer, you can do it from Download CS6 products
You're showing the uninstaller for Photoshop. That won't help with ID....
As far as I know there is no support for CS6 products other than these forums, but you can try the Contact Customer Care link.