"This student really likes geography."
Since 'really' is emphasized in the English, 真 should really be a correct (ideally preferred) translation!
Real =Zhen 真, really or very can be said in many many ways. Hen 很 is but one.
Yes and Duolingo enforces it strictly... until they just say whatever confuse them all...
I think since it is a student we're talking about, it should accept 地理课 if you assume they're referring geography class