Learn Danish: Kan du bære bakken ud i køkkenet? - Can you carry the tray out to the kitchen?

Danish makes a strict distinction between movement and location. Because you are actively moving the tray from one place to another, you use the dynamic word ud (outwards). If the tray was already sitting in the kitchen, you would use the static word ude (out there).

Why do we use i instead of til to say 'to the kitchen'?

When you are entering a clearly enclosed room or building, Danish usually pairs the directional word (ud, ind, etc.) with i (into) rather than til (to). You are carrying the tray out and directly into the kitchen space.

Does bakken mean anything else besides 'the tray'?

Yes, the noun en bakke can mean either a tray or a hill. The context of a kitchen makes it clearly the tray here. Additionally, as a verb, at bakke means to back up or reverse a vehicle.

Could I just use tage instead of bære here?

Absolutely. Kan du tage bakken ud is very natural and common. Using bære (carry) just puts a little more emphasis on the physical effort of lifting and holding it, which makes sense if the tray is loaded with dishes.