"Bu yıl şubat kaç gün?"
Translation:How many days are in February this year?
In English we also say, How many days in February this year. That should perhaps be considered an alternative, although in and is are different.
how many days are in February this year? your sentence doesn't have a verb
First: The standard form of What/How questions starts with how, in this case the order would be "How many days is February this year?"
Second: In English, months "have" days, instead of "being" a certain number of days. So you need to use "How many days does February have this year?" or "How many days are in February this year?"