Restore a SQL Server 2012 backup file in SQL Server 2016/2014
Yes this will work.  You can always go forward, you can't go backwards, at least not with backup and restore.  With older version eg SQL 2000, SQL 2005 sometimes you have to do a stepped upgrade, ie go from 2000 to 2008 to 2014, but that shouldn't be a problem for you.

Be aware when you restore your databases they will have the older database compatibility level.