When checking for updates on Windows Server 2012 R2, you get error 0x80072ee2. 0x80072ee2 is a bit of a generic error meaning that Windows Server 2012 R2 can’t connect to the Windows Update site.
While this can be fixed with a reboot, error 0x80072ee2 can often be fixed as a network issue. Check you have access to the internet, firewall, and all the usual network culprits. In my case, I got error 0x80072ee2 because I had a default gateway issue that was highlighted by an ipconfig but not in the network adapters GUI 😕