Translation:Each of his children has his own room.
This is the flipside of the issue I just talked about on another translation.
That one was too loose and adding a linking verb (are) while changing the tense of the main verb (from work to working), which could potentially change the meaing if given more context. That should have been more strict.
This one should be looser. Their doesn't change the meaning in English in the slightest, even if it isn't the literal translation.
And in fact it's seen as more incorrect in English to assume masculinity nowadays than it is to just use their as a substitute for his/her.
While this was true and many "purists" still cling to that, what is correct is what is actually used by most people and is seen as correct by most people.
These days it's often viewed as wrong to assume masculinity, and thus their is a much more common substitute for the classical he (or she if the writer so chose to assume femininity).
So yes, in old English you would say he, but in modern English the majority say their.
I think this sentence has two parts which are "debated" in English. (1) each has or each have, and (2) his/her own room or their own room. At least according to the below source, it is debated even by usage panels: http://www.grammar.com/each-singular-or-plural/
I think all variants should in principle be accepted.
"Each of his children/sons have his/their own room." is wrong.
Substituting like so:
"Each one has his/their own room." shows that 'have' doesn't work.
It only sounds right in context of the plural 'children/sons' and seemingly plural 'their' (seemingly plural because 'their' is used here to mean a single person of unspecified gender).
"La" is not "his", it's the feminine definite article followed by the feminine form of the adjective "propria" and the feminine noun "stanza".
A literal translation would be "Each of his children has the own room", but that makes no sense in English. Since "proprio/a", meaning "own", implies possession, the possessive pronoun is not needed in Italian, but it is needed in English.
There are some example sentences here: https://blogs.transparent.com/italian/proprio/
The problem with that is the Italian version doesn't use his or her so it would not be a literal translation.
But as I said in another post on this I think this is a case where using "their" or "his or her" instead of just his doesn't change the meaning, and thus they should be acceptable substitutes. They are too strict in this when there is no need to be.
Yet in another translation from this very lesson, they were too loose with translation and actually gave an incorrect English translation (using "are working" instead of "work") in a sentence where the added verb and changed verb tense could actually change the meaning of the sentence.
Italian doesn't have this problem because "propria" agrees with the noun and no possessive pronoun is necessary in the Italian sentence.
So it's a question of what's best in English, and in general, I think we avoid using "it" or "its" to refer to a person. The standard (which I realize is sexist) is to use "his" when we don't know the gender or when we're referring to a member of a mixed group.
But more and more, people are using "they" and "theirs" in these situations instead of just "his" or "his/her" or "his or her", which sound awkward because they are.
While "ognuno" is singular, it refers to each one of the children, so "their" might not sound out of place in this sentence.
Whether or not Duo accepts it is another story.