Hello @MyTokyo0,
When you say you sent your guest a special offer I presume that the guest made an inquiry and you responed on Airbnb by their special offer feature.
If yes, then it's up to the guest to press "accept". They have, I think, 24 hours to do this. If they accept then the booking is made automatically.
If you block the dates for them I believe that they will not be able to accept your offer.
Sending a special offer leaves the days unblocked as you could send special offers to many guests at the same time. The first one to accept would get the reservation.
Airbnb doesn't really allow hosts to treat some guests preferentially. The first one to book wins.
In this situation you would have to turn off instant book and then deny any other guest who booked while you waited for the special offer guest to accept. A risky strategy as a guests often book elsewhere and just not respond to the special offer. You might then end up with no booking.
Steve.