This question has been created to split two questions previously asked here
It is a "hole" in a desk. What can I call this? Can I say "Put your books into the hole"?
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That internal area is called a "compartment". (If it had a container that you could slide out to place your things inside more readily, that would be a "drawer".)
(A "hole" is too generic of a term, and would not be associated with the desk; a "slot" would be a long, narrow hole that allows you to insert, for example, an envelope into an otherwise closed compartment. This desk has a (closed) drawer with a slot.)
The hole in that desk can be called a slot. See this definiton.
Apart from anything else that does not look practical. What would you put in there? Paper? Exercise books?
I would not describe that space as being a slot. A slot is a snug, tight hole, usually horizontal, and just enough space to slide something in. A coin for example. A slot machine, for example is another name for a fruit machine. In that case the coin slot is usually vertical.
I wouldn't call it a hole. A hole tends to be round, not always, but if you were to ask someone to draw a hole in the wall it would be round shaped.
Personally I would call it an "open drawer" or a "paper drawer" or "an open unit" or a "paper storage nook". Google provided this possibility:
Open paper storage drawer The actual piece of furniture is called "a four drawer open paper storage".
But admittedly it is a bit of a mouthful. It would take you longer to say to a friend: " Please put the book into the open paper storage drawer." than to put the actual book away yourself. "Hole" then would be fine, life's too short.