Kevin just returned from an Alaska Cruise and downloaded all the photos and videos, but his Time Machine backup will not complete it due to insufficient free space. Leo says it sounds like his hard drive has run out of room. Even with 20GB of free space, Time Machine may be taking a snapshot of the drive locally, before backing it up. Choices: Free up space on the internal drive or buy a larger one.
The chatroom says that if the external drive can't be seen, Time Machine will make the backup locally. So make sure it can see the external drive.
Leo also recommends not solely relying on Time Machine for backup. Get an external drive about 4TB and use a program like SuperDuper to make a bootable external backup, which Kevin can boot to in case something happens.