Translation:The young girl walks through the house.
Door can have the meaning around (throughout, to and fro within) as well as directly through as in "in the front door and out the back door" so I guess it all depends on context. Walk through the house can mean walk around within the house in English, so I guess both possibilities are covered.
"Door" can mean "by" in the sense of "the means or person by which the action is carried out". Examples online include De vaas wordt door Jan gebroken ("the vase is broken by Jan") and Hij vermeed een confrontatie door de andere kant op te lopen ("He avoided a confrontation by walking the other way"). In the context of this exercise it can't mean "by".