とおす
to let pass, to run through
You make the thing go the whole way through rather than standing there watching it. Thread through a needle, and the same tour とお as 通り straight down it: とおす.
通る とおる is a thing passing through by itself. 通す is you putting it through.
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Emaki is not affiliated with, or endorsed by, Kaishi 1.5k or its authors. The word, reading and meaning come from the Kaishi 1.5k deck, used with their permission. The mnemonic, the note and the kanji breakdown are original work, published under CC BY-SA 4.0.