for the life of you

US /fɔr ðə laɪf əv ju/
UK /fɔr ðə laɪf əv ju/
"for the life of you" picture
1.

even with the greatest effort; used to emphasize that someone cannot do something

:
I can't remember his name for the life of me.
She couldn't understand why he did it for the life of her.