What does I'll show you my kates if you show me your William mean?

The phrase "I'll show you my kates if you show me your William" is a playful reference to the popular children's game "show and tell." It suggests a mutual exchange of personal items or stories, with "kates" possibly referring to something specific to the speaker and "William" to something meaningful to the other person. The phrase can also imply a sense of camaraderie or openness in sharing aspects of one's life. Overall, it's about mutual sharing and engaging with one another.