@Christine333.....I would love to say there is some way I could help you but, I am afraid Christine, you have been your own worst enemy.
You must read the rules of hosting before you do something that will affect you badly!
You cannot cancel a guests booking!!! The fact that they might have had email problems is no excuse, they had booked your listing and had every right to expect that booking to be honoured.
Airbnb are really firm on host cancellations because it can have a catastrophic effect on guests. When a guest books a listing they, in many instances, will come from far away, and make other travel plans to tie in with their accommodation.
In days gone by hosts would cancel confirmed bookings if a better offer came along and the whole site suffered badly, so now there are strict rules that must be followed.
The penalties you will now have to face are...
1/. The days that this guest had booked for will be blocked on your calendar preventing you from accepting another booking.
2/. You will suffer a financial penalty which will be taken from your future hostings!
3/. You will be inelligible for Superhost status for one year from the date of the cancellation.
4/. On your reviews an automated posting will be placed that says 'this booking was cancelled by the host .....days before arrival'! And this can be the kiss of death because guests tend to stay clear of hosts who cancel bookings.
Possibly there can be a silver lining Christine! I would suggest you contact Airbnb in Sydney on 02 8520 3333 and explain to them that, as a first timer, you were not aware of the proper protocol and deeply regret your action and ask them to re-instate this booking....provided the guest still wants to book. You will find the Sydney office efficient and helpfull and you may be able to get some relief from this situation.
Yours is not the first post that details exactly this situation....in fact you would be amazed at how common this scenario is, and it all comes about because new hosts do not read up on what they should do in order to host. You will find at the top of this page a box that says 'Search for Anything' Please type in...'How do I get paid'....'How do I confirm a booking' .... Difference between a booking enquiry and a booking request'....'Guest and host cancellations'...'How do I contact Airbnb'
Try and understand the framework that this platform operates under.
It's better to have information and not need it than to need information and not have it!!!
Cheers....Rob