Give your eye teeth for something/to do something - Idioms by The Free Dictionary
give your eye teeth for something/to do something
give (one's) eye teeth for (something)
To give or relinquish anything (or something very valuable) in order to receive some specific thing in return. Oh, I would give my eye teeth for curly hair like yours.
give your eye ˈteeth for something/to do something (informal) (usually used with would) give anything for something; want something very much: I’d give my eye teeth to own a car like that. ♢ He’d give his eye teeth for a job in television.