The (localdb)\ProjectsV12 and (localdb)\ProjectsV13 instances are created by SQL Server Data Tools (SSDT) and should not be used by applications
(localdb)\MSSQLLocalDB is the SQL Server Express 2014/2016 LocalDB default instance name and an “automatic instance”.
You can use the sqllocaldb.exe command line tool to manage which version (2014 or 2016) owns the MSSqlLocaldb instance
And (localdb)\v11.0 is the SQL Server 2012 LocalDB default instance name