The problem is that learning programs often have intentions, ideas behind certain sentences. In that case, they wanted to communicate a sentence that includes the girl showing of possession. Therefore they need you to use 'own' as translation here. The problem is, that there is no given context and so any translation is supposed to be correct here, as long as it suits the translations possible for 'proprio'. A problem most of the learning programs have, unfortunately.
Proprio -> exact, real, proper, own, peculiar, real, typical
Now we all know that common sentences are not what we are used to @ duolingo. They mix up weird things that people often wouldn't say in reality, because its their way to brand words into the learners minds. Absolutely fine to me. It's nice to have some funny sentences from time to time, as they seem more remarkable. But why do you mark proper plate as wrong then? hm? Is there some kind of intention behind that sentence? If yes, how would the learner know, when he doesn't even get the word 'own' shown when moving the cursor onto 'proprio', which is obviously linked to 'proper'? Why wouldn't you rather accept proper as translation, because it is a correct translation, as the sentence is not set into context. And while accepting it, you could point on the more common meaning, if it is like that, 'own'.
It could look like this (assuming Italians use 'proprio' primarily with the meaning 'own') : 'You chose 'proper' as a translation for 'proprio' - seems like intuitively recognized their similarity - their derivation from the Latin language - nice! But please keep in mind, that Italian people would rather use the word to indicate Possession. Therefore, 'own' would be a better translation here.'
This would actually help people. But when words are marked wrong, that are shown by the software itself as correct before, it is pain in the ass. Especially when you intuitively saw connections between words, like the above mentioned derivation.
Have a good time all!
Confusing? Yes. Even though the possessive adjective (proprio) must agree with the thing or object possessed (il piatto), the subject or possessor is female, so the possessive pronoun would be "her" not "its." "Il raggazzo ha il proprio piatto." The possessive pronoun would be "his plate." Hope that's clearer.