That kind/sort; that way (of doing things). A colloquial expression meaning 'that type' or 'that manner'.
その手の話はもう聞き飽きた。
I'm tired of hearing that kind of story.
その手の仕事は彼に任せておけば安心だ。
You can leave that sort of work to him with confidence.
その手の本は若者に人気がある。
Books of that type are popular with young people.
That move/trick — a specific tactic, trick, or gambit (often in games or strategy).
将棋でそんなその手があるとは知らなかった。
I didn't know there was such a move in shogi.
あの営業マンはその手のテクニックに長けている。
That salesperson is skilled in such techniques/tricks.
その手に引っかかるな。
Don't fall for that trick.