After upgrading to the new MacOS Mojave, the FaceTime might not working correctly. Take following solution to fix.
After checking your internet connection and disable/enable Face Time, if the situation remains the same, the following tips would help:
Solution 1: Verify Phone number or Email address
Make sure that your email address or phone number, which are registered in FaceTime is correct.
Solution 2: Correct the time zone
FaceTime > Preferences and check the Apple ID.
This solution would help too many users to fix FaceTime not working not only under MacOS Mojave, but all other older MacOS Versions.
Open the Apple menu and go to “System Preferences” > “Date & Time” > turn on ““ Set Automatically ” to set Time Zone to your current location.
Solution 3: Improve the internet connection by Changing DNS setting
Facetime need internet to work of course. In some cases, your current internet seems to work well, but there is still the possibility of that you can not connect to Apple’s servers by reasons. I would suggest to use the DNS of Google.
Open the Apple menu and go to “System Preferences” > “Network” > select the using Wi-Fi then tap “Advanced” > open “DNS” tab > Click on (+) button to add “Google DNS” > Enter 18.104.22.168 and 22.214.171.124 and “Apply” changes.
Please contribute your fix to help the others.