I am from California and here we don't hear "Listen properly!" We say "Listen carefully!" There are different nuances with each though and I would completely understand "Listen well!" even though it is less common here.
I am from Germany and i at first thought also about giving the answer "listen carefully". I then refrained from it, becaus i did not want to provoke to get a "wrong" from Duo. So now i am relieved, that even native English speakers would give this answer.