"My duck does not want to eat you."
Translation:הברווז שלי לא רוצה לאכול אתכם.
Etkhem is not wrong, it’s the given translation. Etkhen would be correct if the speaker were talking to a group of girls and/or women.
Otkha would be correct if the speaker were talking to one male (a boy or man).
Otakh would be correct if the speaker were talking to one female (a girl or woman).
Duolingo should accept all these answers because which one is correct is not clear from the English word “you”.
Even though ברווזי is correct, using pronominal suffixes is considered very formal and they have become rather rare in everyday language, apart from a few exceptions (some body parts, some family members and some fixed phrases). This is also the case in this course - pronominal suffixes are not used in the course, except for the skill "Possessives 2" and several fixed phrases occurring in the course here and there.