"남자는 모자를 주웠어요."
Translation:The man picked up his hat.
"남자는 자기의 모자를 주웠어요" This sentence can only be translated to "the man picks up his hat" but the one in the question can be either translated to give the last meaning or to "the man picks up the hat" so why is it wrong!!
I am a Korean. You are right but you have to select only 'his' for the answer.
모자 can mean hat or cap, but the computer will not accept cap. Also, nothing in this sentence says he picked up HIS hat. If he is in a store to buy a hat, the sentence could mean the man picked up a hat.