Learn German: Kannst du die Lampe auf den Schreibtisch stellen?

stellen means to place or put something in an upright position. We use it here because you are actively moving the lamp. If you were just describing where the lamp already is, you would use stehen (to stand).

Why is it auf den Schreibtisch and not auf dem Schreibtisch?

Because auf is a two-way preposition. When an action involves movement towards a destination (like putting the lamp onto the desk), we use the accusative case, which makes the masculine der become den. If the lamp were already sitting on the desk, we would use the dative case (dem) to show a fixed location.

Why is stellen at the very end of the sentence?

This is a yes/no question using the modal verb können (kannst). In German, the conjugated modal verb goes first in a yes/no question, and it pushes the main action verb (stellen) all the way to the end in its infinitive (dictionary) form.

Could I use legen or setzen instead of stellen for the lamp?

Usually not. Because a desk lamp has a base and stands upright, it is placed vertically, so you use stellen. You would use legen (to lay) for something flat like a piece of paper, and setzen (to sit) mostly for people or animals.