I would like to know the meaning of the next sentence.
I guess I showed her!
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The expression "That'll show you" or in this case, "I guess I showed her" means "This will demonstrate who is smarter, stronger, right, etc."
The humor is that the boss thinks he won the argument, but she spend a lot of his money to buy herself something, so she really won.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.