"Péter is in the hospital."
Translation:Péter kórházban van.
It's awkward, because American English is really inconsistent: in school, in college, in jail/court/prison, at lunch, at work, at sea, in flight, in office (political) are OK everywhere, but not at university, in hospital (those are British only) and definitely not at doctor, at job, at store, at ocean (all require an article, even in England, I think)
In English, Péter is in the hospital usually means that he's in a generic hospital. I'm assuming that it is marked wrong because the same construct in Hungarian would mean that he is in a specific hospital.
Ones like this are a bit tricky, and depend on context. But (assuming I'm right with the above) it's probably correct for Duolingo to mark off. If you meant a specific hospital, you'd probably name it...
It's hard to tell with Duolingo; sometimes you need to translate something very literally, even if it's a little awkward or has a slightly different meaning in the other language, and other times you're marked wrong for being too literal. (For example, many languages use the definite "the [noun]" to mean the equivalent of English's indefinite "[nouns]" but Duolingo rarely accepts such a translation.) I think both "a kórházban" and "kórházban" should be accepted here.