"Omar is Omani American."
Translation:عُمَر أَمريكِيّ عُمانِيّ.
The order of adjectives in Arabic is the reverse of that in English. In English, the most relevant adjective comes just before the noun. In Arabic, the most relevant adjective comes right after the noun.
Of course here the two adjectives (Omani and American) are predicative and do not come before a noun, but you can imagine some noun after them (e.g. "man"); It doesn't change much in the meaning.
So, in a nutshell, Omani American in Arabic would be literally amriki/3omani in order, because the person is now American (most relevant) and his origins are from Oman.
Don't worry much about that; It's Duolingo's fault.
The name for America (and consequently, American) in Arabic can be written in two ways: Either as أمريكا (amríka) or as أميركا (amírká); The difference is just in flipping the the (R) and the long vowel (í). The second mimics how it sounds in English, hence it is (amírká), and despite having (í) ي here but usually people who use this version do in fact say it more like amérká rather than amírká. Probably this version is more common in the Levant.
Anyway, I'm not sure why Duolingo is marking a typo here as I see you typed it exactly as mentioned here already, but well, it's Duolingo. After about 3 years in it, I think I got used to its quirks.