I am doing a lot of AX databases restores weekly, as part of the TEST to DEV machine's update process, and I always use the UI approach, which tends to take several minutes (clicking your way through the screens). Not that it's too much time to loose, but, I figured this is much faster. So, the most simple way, the T-SQL statement:
Of course, I will remind you, never use these in a PROD environment.
drop database MicrosoftDynamicsAx
restore database MicrosoftDynamicsAx from disk='C:\Data.bak'
drop database MicrosoftDynamicsAx_model
restore database MicrosoftDynamicsAx_model from disk='C:\Model.bak'