Facebook securiy check: sms or photo verification?

Hi,

I will soon move to another place and buy a new PC, in a few days.
When I log into Facebook from a new device, I am asked to identify friends based on pitcures. The problem is that more than once I almost failed this test, as Facebook was showing pictures of sceneries or animals to recognize.
But I still have my account.
Thus, I would like to avoid this verification to happen on my new PC and the risk to lose my account.
Hence I activated the two-step validation on the purpose that Facebook sends me a validation code via sms, thus being able to verify my identity when connecting from another PC…
Would this avoid the picture identifying test? Or will Facebook still ask me to perform this test it after asking my password and sms sent code?
Do you know about a way to get bypas this test?

Thanks a lot in advance, and have a nice evening!