How to activate the half booking days ?

It's possible at the Booking Calendar Business Small and Business Medium versions of Booking Calendar in update 4.1 or newer.

You can activate "Use check in/out time:" option at the General Booking Settings page.
Then in the sub-settings set the "Check in" time as 15:00 and "Check out" time as 10:00. (You can set the different times there, but be sure to set the "Check In" time older than "Check Out").
Save the settings page.

Now, your visitors will be able to use the same date as check in/out date for the different bookings, its mean if the some booking is finished on the specific date, other visitor can start the new booking on the same specific date.
The check in/out days in calendar will be marked as half booked (diagonal line) and not by clock icon as for the usual timeslots.

Please note, this option will apply globally to the all booking resources and will overwrite any time slots, if you will use them in the booking form.

If you are need to use just time slots in the booking form, so you are need to deactivate this option and configure the time slot selection at the Booking > Settings > Fields page. Please read more about the booking form fields configuration here.