Like other prepositions, there are many different ways of signing "through".
ASL signs for THROUGH
How to sign "through" in American Sign Language (ASL)?
Meaning: Continuing in time toward completion of (a process or period); moving in one side and out of the other side of (an opening, channel, or location).
Pronunciation (sign description): Dominant horizontal flat hand with palm facing left moves through non-dominant upright flat hand between forefinger and middle finger or sometimes between middle finger and ring finger (phonological variation).
Old ASL
"Through -- Push the right "B" hand edgewise outward between the middle and third fingers of the left, which are open and closed over against the forefinger and little finger respectively, and pointing upward." (1910) Ref
Beyond basics: Phrases
"go through"
Meaning: to experience something especially a difficult or unpleasant situation.
Context or usage examples: "had to experience many challenges in his/her life" (glossed as "HAVE-TO LIVE/LIFE EXPERIENCE THROUGH-cs CHALLENGE+++").
Meaning: during the entire period of. E.g. "all through her life". Use ALL with modified intonation.
Beyond basics: Classifiers
For prepositions in ASL, classifiers are heavily used. Learn and understand how to use classifiers first, then you'd be able to use classifiers without looking up.
Examples of using classifiers for the English translations: "drove a screw through the wood board", "drove through a red light",
