Note: After form submission, the process is quite quick and you may need to follow up directly with Booking.com either via Extranet Inbox or call to acquire the Legal Entity ID. (if they haven't reached out to you already).
Once you get your Legal Entity ID, you can set in on the Booking.com Channel Management page on Hostfully at https://www.platfom.hostfully.com/channels/bookingdotcom/synch.jsp :
click on the link as shown below
enter the Legal Entity ID in the field