Using Oracle12C Client with Oracle11.g database I have been using Oracle12c client to connect to an Oracle11g database in a remote server for about one month, it wasn't giving me any problems until this week, when I started getting the error:


  The Network Adapter could not establish the connection Provider Code 17002


First I used Oracle Sql Developer to design the tables of the database, and a week after that I started to develop an app with Visual Studio 2013, where I used the native adapter and the library Oracle.DataBase.Client as part of the Visual Studio Integrated Tools that oracle provide to work with their databases. 

I would like to know if the errors could be because the client is 12c and the database is 11g or if this question doesn't matter and another thing can be happening.
The document that has the client/server compatibility matrix is 207303.1 Client / Server / Interoperability Support Matrix For Different Oracle Versions. (Oracle support account required)

Oracle client version 12c is compatible with Oracle server version 11.2 (and below), so no your error isn't likely to come from that.

Check that the listener is indeed started on the database server, check that the database is up, and check that the database is registered with the listener.