Answer by Professional Japanese Teacher
(You) first, please.
You can use the above expression. Osakini literally means “you go first”. It is used when you want other people to go ahead first with whatever they are doing.
You can also use this expression when you are holding the door to a restaurant, shop, or even your office. If someone says Osakini doozo, you can reply “ありがとうございます Arigatoo gozaimasu (Thank you)”.