Answer:
The preposition is "through".
Step-by-step explanation:
In the sentence "Jaime walked cautiously through the dark alley", the preposition is the word "through".
A preposition is usually a short word employed to make a connection between other words, that is, to establish a relationship between words. Examples of prepositions are: by, on, in, at, around, above, below, through, out etc.
The preposition "through" commonly appears before a noun and after a verb that indicates movement. This preposition means something moves in one side and out the other side of something, usually a location. In the sentence we are studying here, Jaime walked in one side of the alley and out the other, which means he walked through the alley.