I wrote "I have a special vegetable on a plate" - since that was wrong because I didn't specify it was 'my' plate, how would one write the sentence I wrote in English?
Your translation is correct if you only look at the written sentence, without nikkud. If you listen to the audio, he says batsalachat and not betsalachat. Literally "in the plate" which can be understood as "in my plate", but not "in a plate". Hope this helps.
It doesn't necessarily mean that it's one's plate if one merely specifies a definite plate.
I think Duo's "correction" and "marking us wrong" are both incorrect.
Even, I don't think this correction of Duo is valid as an option either.