Double booking


i have a double booking 18-22 of july

it happened when I released a new property and I got swamped with bookings 

first i got a booking for the exact same dated in airbnb, and I didnt manage to lock the dates in booking.com

i havent managed to syncronize the calendar either as I found it very difficult with the instructions. I have locked the dates manually on both my properties up until yesterday as I actually managed to synvronice the other propertys calandars, but still not the one with the double booking

with this i come to a second problem

if i lock a date in either airbnb or booking.com in the synvronized calandar it doesnt show in the other even if i clicked in the option of ”show locked dates”I tried one time in booking and one time in airbnb, but it remains unlocked in the one that i didnt lock

To the first problem. I didnt tell the guest right a way about the double booking as I wanted to offer the airbnb guest to stay in our privat home (us away) because they wanted to book longer then we had avaliable dates. 
but they didnt want this, so now I need help from you. Can I offer the booking guest to stay in our house? What happens if they dont want that?