"They eat their own cake."
Translation:Loro mangiano la propria torta.
I wouldn't say that it's wrong, but it's kind of rare, especially in the third persons. There's an article on the Crusca's Q&A that mentions the case of "sua propria". Using both the possessive and proprio adds emphasis, so it's similar to how in English you could say "their very own cake".
No, the hint is for the masculine form. From the word "torta" you need to work out that you need the feminine form "propria".
This gets me a lot of the time too, especially if I'm not thinking clearly late at night. Personally I think it's a good thing and I learn more.
DuoLingo tends to mark "incorrect" if it believes you are conjugating a word incorrectly or using the wrong word. If your spelling error caused either of those things by mistake, it would be marked as wrong automatically even if it was just a typo on your end. For example, I've written "capello" (hair) instead of "cappello" (hat) before by mistake and lost the whole question because - even though it was a spelling mistake of one letter - I actually accidentally wrote another word that wasn't correct for the sentence (and the program can't tell what my intention was behind it). Your case may be different, of course, but I've found it's generally like this.
Hi Judi... in theory you are right. However.... the Italian language does drop io, tu, lei, lui, noi, voi loro as being unnecessary as the verb conjugation indicates the pronoun i.e iamo, iete, o, i etc. When you are first starting to learn Italian it is a good reminder that' iano' is linked to 'loro', 'iamo' is linked to 'noi', 'o' is linked to 'io' etc... it is not wrong but also it is not usually used (unless emphasising a person or persons). Idiosyncratic if you speak English but not if you are Italian. When you get fluent you will drop the pronoun automatically but if you use the pronoun and speak it you will be understood by an Italian. Hope that is a bit of help.