As pointed out by MacRumors, beta versions of Mojave started to alert users that Back to My Mac will end soon. An Apple support document (posted on August 9, 2018) confirms that the feature will not be supported in Mojave.
What is Back to My Mac? It allows users to remotely access Macs to perform file sharing and screen sharing. It requires the Macs involved to use the same iCloud account and run at least OS X 10.7.5 Lion.
If you simply want to transfer a file from one Mac to another on the same network, you can use AirDrop
You can also use a third-party online file storage/sync service, such as Dropbox, Microsoft OneDrive, or Google Drive. You’ll have to rely on the service’s software or browser interface, though.
MacOS has a screen sharing feature built in. You can find it under System Preferences > Sharing. In the box to the left, mark the checkbox for Screen Sharing. You can specify what users can perform screen sharing, or all access for all users. Here are the details for setting up screen sharing.