If a member claims to have booked on an event, but you can't find the booking, there are a few possibilities:
They booked on the wrong event
To check if this is the case, go to the member's page in the admin panel. Scroll down to the orders section to see what bookings they have made.
If they have booked on the wrong event, cancel the order that they had placed, and ask them to book again (if they have not yet paid), or place an order on their behalf for the correct event.
They didn't complete the order
To check if this might be the case, go to the member's page in the admin panel. In the left hand column, check the date that they last signed in. Then check the order section to see if they placed an order on that date. Chances are, if they logged in but didn't place an order, that they never completed the checkout process.
If this is the case, ask them to place an order for the event.