After installing/enabling the two-way authenticator in Joomla you might come into a problem with Googles Authenticator: 

If the Google Authenticator does not work in Joomla,

Synchronize time correction for codes in Google Authenticator

Good advice.

This has to be done from time to time. You'll know when,  because you can't login. Go to Settings->Time correction for Codes. See pics below: