The kids were having a hard time putting their handouts in their binders.
この場合、次のような言い方ができますよ。
ーThe kids were having a hard time putting their handouts in their binders.
「子供たちはプリントをファイルに綴るのに手こずっていた」
to have a hard time で「手こずる」
handouts で「プリント」
to put ... in binders で「ファイルに…を綴る」
ご参考まで!