.bak file not visible for restoration
You did not save the files where you think you did. 

In the first image there are 9 folders below 'Microsoft SQL Server' and above 'MSSQL11.MSSQLSERVER'  in the second screen shot there are only 5.  

This is possibly an issues with your local machine VS a seperate server. Assuming the address you are following are identical (C:\Program Files (x86)\Microsoft SQL Server\MSSQL11.MSSQLSERVER\MSSQL\Backup) the only solution remaining is that the C drives are on different machines.