"Ho una tazza."
cup or mug is a better translation of tazza. I'm not sure why they even have bowl in the hover hints as I have never heard tazza used to mean bowl.
Generally the first option Duolingo gives on the hover hint is the best one to pick, as not all of the hover hints are appropriate for every situtation. (Possibly tazza means bowl occasionally, when used in a specific situations, or something like that. I don't know. What I do know, is that cup or mug is the usual translation for tazza)