Asks which day of the month or which date (e.g., "What day is it?"). Used to ask for a specific calendar day.
試験は今月の何日ですか？
What day is the exam this month?
誕生日は何日ですか？
What day is your birthday?
会議を何日にしますか？
Which day shall we set the meeting for?
Asks how many days (duration). Used to ask about the length of time in days (e.g., "How many days will it take?").
旅行は何日ぐらい行く予定ですか？
How many days do you plan to travel for?
レンタカーを何日借りますか？
For how many days will you rent the car?
直すのに何日かかりますか？
How many days will the repair take?