"I am very happy to meet you."
Translation:Je suis très heureux de vous connaître.
Just my two cents and I don't know if this assumption is right: Perhaps "rencontrer" is used in the sense of, "Hey, do you want to meet at 5:00?" rather than meeting someone as in being introduced to them. So they both mean "meet" but since they are in different contexts, the French may have individual words that translate to each of those meanings. (I got it wrong also!)
That's gotta hurt (especially as I can find numerous examples of 'très enchanté' in French texts). My reckoning was: enchanté = delighted = very happy. Maybe Duo thought that 'très enchanté' was over-egging the pudding? No one has ever been very delighted to meet me... but on the other hand, it could be that I'm not very delightful.
As others have said, 'Je suis très heureux de vous rencontrer' should, surely, be accepted (given the lack of any other contextualising material).
It's idiomatic (natural) in French to use "connaître" in expressing this sentiment when meeting someone for the first time, but it's not normal in English to use "know", so "connaître" doesn't bear a direct translation.
And we have confirmation on this discussion page from a native French speaker that it's also natural to use "rencontrer" when meeting someone for the first time (i.e. both "connaître" and "rencontrer" are correct here):
In case anyone else is wondering: