"Give the child one ball."
Translation:아이에게 공 한 개를 주십시오.
하나 is used for counting--such as one, two, three whereas the short form for one (한) is used for saying how many. Process can be found in the Duolingo Tips for this session. Accordingly, the correct application for this sentence is (곻 한 - one ball). The general format for the application is Noun + Number + Counter + Particle as noted by the solution.