The answer is March 15

Roi is given the day and Josef is given the month. This is because Josef can only know the month is he is given a unique month but there are none. Roi can only know the date if he has a unique day, the two are 17 and 18. So if Josef says Roi doesnt know then the months corresponding to these dates are eliminated
Jan 14,15,18 and Feb 16,17,13,15 are gone

So we are left with March 13,15 and Dec 13,14,16 meaning Roi has either a 13,14,15 or 16. It cannot be 13 because there is not enough information. That leaves Dec 14 and 16 and March 15. It cannot be either December date because there is not enough information so the answer has to be March 15