@Love223 There are three approaches.
1) If you wish to be very courteous: Ask the guest to cancel their stay. Explain that unfortunately you have no way to get the nights totally 'back' and recover their value, as other guests have been unable to book them since he/she made his booking. But as a courtesy, let them know that if you succeed in getting any replacement bookings that cover any of the same nights as their original booking, you will be happy to refund them any 'replacement' money you earn that way for those same nights, after you have received it and covered your expenses.
This phrasing is very careful. You are offering to give back the money from the new bookings that applies to any of those same original nights. You are not offering to send back all the money from any reservation that covers ANY of those nights. Why not? Well, imagine the original guest had booked for 2 nights. He cancels. A new guest books for a week STARTING on the original guest's 2nd night. You should not be on the hook to return the entire week's new rent for the sake of that one recovered night. Instead, you'd be returning just the portion of the new rent (say, one seventh) that applied the night recovered from the first guest.
2) As an alternative, you could make it more like a mutually profitable business deal: "Unfortunately, even if you cancel now, I likely cannot fully recover the revenue of the period you had booked for, since those dates have been blocked for other guests. But if you will cancel your reservation now, that would open up my calendar. I'll try to get some replacement bookings for the nights that opens up. If I do, then I'll refund you half of whatever rent I receive for those nights from any new bookings I receive."
This approach is a kind of win-win. It splits the difference between you and the guest. The situation remains profitable to you, since you will definitely get to keep the original guest's rent and may also keep half of any replacement rent as well. But it also gives the guest an incentive to cancel and open up your calendar, since only if he does so does he/she stand to get back some of what he paid.
3) Of course, you could just acknowledge that it was an understandable mistake and offer a full refund if they immediately cancel. This means you very definitely take a financial hit. But maybe it is worth it, for the chance to be gracious.
Most recently when I was in this situation, I personally took approach #1. The guest declined the offer and it turned into a bit of a kerfuffle, because of course the guest (who then actually showed up!) was not happy to be in the property. But I was very careful to document things with AirBnb Support, as they happened, and other than a lost hour or two of my time, nothing else bad came of it.
