The correct answers are The old pizza box is under the bed. and The dirty shoes are next to the door.

Let's look at the rules!

• Under means directly below something (under the bed). We don't say "under to".

• Next to means right beside something (next to the door).

• Between needs at least two things to be in the middle of (e.g., between the desk and the bed). You can't be "between" just one desk!