You should be able to cancel a booking in your channel manager and this cancellation will be sent thorugh to Hostelworld Inbox. The Hostelworld API is able to receive cancellations directly from your channel manager/property management system via 'setcancellation' call.
Hostelworld provides this function to all channel managers. Please contact your channel manager or property management system to get that activated for you.
* If your channel manager does not support Hostelworld 'setcancellation' call, please contact them directly to enquire about a possible implementation date.
**Bookings can only be cancelled if the customer requested the cancellation. In case of an accidental overbooking, you will need to agree a solution with the cutomer : relocate them or refund their deposit, before you can cancel the booking.