You need the preposition, "by" in your sentence.
The word, through, also a preposition, can describe travelling from place to place.
For example, "the train travelled through the tunnel" or "he walked through the doorway".
It can be used to explain how water moves.
For example, "the water soaked through the coat" or "the water went through the tap".
The word can also be used to describe the end of something.
For example, you could ask, "are you through with my pen" or "he is through with school for the year".
Hope this is helpful