"an Arab American man"
Translation:رَجُل أَمْريكِيّ عَرَبِيّ
Since the adjective أمريكي came first in the Arabic sentence, it should come first in the English sentence. An American Arab man.
That's not how we say it. The Americans in particular in their newspapers. put people's ethnic origin first for these i.e. African-American, Jewish-American, Indian-American.