The Sync framework can synchronize files across the network as long as you have an available network share.
In the constructor of the FileSyncProvider set the rootDirectoryPath to a network share location that you have read and write permissions to:
string networkPath = @"\\machinename\sharedfolderlocation";
FileSyncProvidor provider = new FileSyncProvider(networkPath);
To do a two way sync in this fashion you will need to create a FileSyncProvider for both the source and destination systems and use the SyncOrchestrator to do the heavy lifting for you.
An example:
string firstLocation = @"\\sourcemachine\sourceshare";
string secondLocation = @"\\sourcemachine2\sourceshare2";
FileSyncProvidor firstProvider = new FileSyncProvider(firstLocation);
FileSyncProvidor secondProvider = new FileSyncProvider(secondLocation);
SyncOrchestrator orchestrator = new SyncOrchestrator();
orchestrator.LocalProvider = firstProvider;
orchestrator.RemoteProvider = secondProvider;
orchestrator.Direction = SyncDirectionOrder.DownloadAndUpload;
What this does is define two filesync providers and the orchestrator will sync the files in both directions. It tracks creates, modifications, and deletes of files in the directories set in the providers.
All that is needed at this point is to call Synchronize on the SyncOrchestrator:
orchestrator.Synchronize();