To shake one's head (to indicate denial or refusal); to move the head side to side in negation.
頼まれた仕事はできないと彼は首を振り、頭を振った。
He shook his head, indicating he couldn't do the requested job.
冗談だよと言っても、彼女は頭を振って真剣な顔を崩さなかった。
Even when I said it was a joke, she shook her head and kept a serious face.
質問に答えられない学生が困ったように頭を振った。
A student who couldn't answer the question shook their head in embarrassment.