頭あたまを捻ひねる

expression, godan verb (-ru)

puzzle over; rack one's brains; think deeply about

Used when someone is struggling to solve a problem, come up with an idea, or understand something difficult. Often implies a visible effort of thinking.

• 難むずかしい問もん題だいに頭あたまを捻ひねっている。

  I'm racking my brains over a difficult problem.

• 彼かれはいいアイデアを出だそうと頭あたまをひねった。

  He puzzled over it, trying to come up with a good idea.