An unreasonable demand or an unexpected, difficult request; a colloquial term for being put on the spot with something unfair or unprepared.
会議中に上司からむちゃぶりをされて、うまく答えられなかった。
I was put on the spot by my boss during the meeting and couldn't answer well.
友達のむちゃぶりでカラオケで一曲歌う羽目になった。
Because of a friend's unreasonable request, I ended up having to sing a song at karaoke.
司会者が芸人にむちゃぶりをして、その場が盛り上がった。
The host made an unreasonable demand of the comedian, and the audience livened up.
客の突然のむちゃぶりには、断る勇気も必要だ。
You sometimes need the courage to refuse a customer's unreasonable request.