This one really threw me. Not only was it the first exposure to a question like this, but it is a strange thing to ask in general. Why would you ask someone else whether or not you like a duck? Maybe something like "Do you eat duck" or "Can I drink beer" would have been better.
One clue is the question mark and the verb came before ich. The "Do" makes sense for English translation of this question.
(As for when would I use this sentence...trying to make a decision at the grocers or if you were deciding which picture of a duck you might use to illustrate an animation. Context makes it sensible.)
It is not clear to me in the statement: Mag ich die Ente? that it implies: Do you like the duck? I wrote, I like the duck, which was wrong. I'm confused. In a sentence that is a question, what's the trigger to know when you add "do I, or, do you" at the start of it?