How to restore SQL Server 2014 backup in SQL Server 2008

No, it is not possible. Stack Overflow wants me to answer with a longer answer, so I will say no again.

Documentation: https://docs.microsoft.com/en-us/sql/t-sql/statements/backup-transact-sql#compatibility

Backups that are created by more recent version of SQL Server cannot be restored in earlier versions of SQL Server.

It is a pretty old post, but I just had to do it today. I just right-clicked database from SQL2014 and selected Export Data option and that helped me to move data to SQL2012.

Not really as far as I know but here are couple things you can try.

Third party tools: Create empty database on 2008 instance and use third party tools such as ApexSQL Diff and Data Diff to synchronize schema and tables.

Just use these (or any other on the market such as Red Gate, Idera, Dev Art, there are many similar) in trial mode to get the job done.

Generate scripts: Go to Tasks -> Generate Scripts, select option to script the data too and execute it on 2008 instance. Works just fine but note that script order is something you must be careful about. By default scripts are not ordered to take dependencies into account.