"Chi ha la direzione?"
Just looked it up on some dictionaries, direzione can translate to leadership or mangagement, so maybe its most natural translation would be one closer to "Who is leading/managing?" or "Who is the leader/manager?" Even "Who has the leadership" would work probably work better than the duo's suggested translation, but I'm not sure. We need a native speaker to help clarify :)
I'm a native speaker of English and "Who has the direction?" is not proper English. I understand that there are some very weird, contextually marginal sentences here on Duolinguo, but this is pushing the limit. Is there a native Italian speaker who can let us know whether this means, "Who knows the way?" (as @Peter2108 suggests) and/or "Who has the directions?" (which was marked wrong for me), or "Who is directing/ Who is in charge? Thanks! :-)