This is the 525th most frequent Russian word.
каким
The word "каким" in Russian is the instrumental case of "какой" and means "what kind of" or "which" (in the instrumental case).
Here, 'каким' is used to ask about the manner or method of something happening.
Каким образом это произошло?
How did this happen?
In this sentence, 'каким' is used to inquire about a characteristic (color) of the wall.
Каким цветом ты предпочитаешь стену?
What color do you prefer for the wall?
In this example, 'каким' is part of a subordinate clause describing the transformed state of a person after a trip.