(slang, usually in plural) A fist.Put up your dukes!This is thought to be derived from where Duke(s) of York = Fork. Fork is itself cockney slang for hand, and thus fist.
It seems that PI Rainer was duked by his wife and he explores his feelings of being on the receiving end of a beating with the gal who is the object of their $300 case, Leila Burnett ... .