@Pat360 You as a host can refund a guest if you choose to. You just go to the Resolution Center in your hosting account and use the "send money" option. Whatever you send will be deducted from your next reservations.
What happened here, it sounds like, is that Airbnb upheld the cancellation policy you have in place, which you should be grateful for. They don't always do that-a guest demands a refund, the host is unwilling to agree to that for whatever reason, and Airbnb overrides the host's cancellation policy and refunds the guest anyway.
As it's obvious that she cancelled after the 48 hour free cancellation period, she will not get back the Airbnb guest fees charged. If she doesn't understand that, you'll need to explain that to her, that those fees have nothing to do with the host- we don't set them, Airbnb does, and we don't see any of that money- it's Airbnb's.
So if you want to refund her, you can certainly do so, just don't include those Airbnb fees in the 50% you are talking about refunding. That's just her loss for cancelling late and nothing you can do about it.