Q / What is the relation between Hat and Duality in Waiting for Godot? Explain elaborately?

I'm sorry, you are referring to the "hats" worn by the characters?

The bowler hats worn by each of the characters serve as a symbol of the human condition in its different forms. Each of the four actors wear similar hats on stage, and it is believed that through this, Beckett identifies each of them, as various representations of the human condition.

One example of this can be found in Act I, when Pozzo tells Lucky to think and hands him his hat, inferring that he needs his hat to think. Lucky attempts to resist the demand and is then attacked by the others.... thus in the end, he recites his text quickly and unintelligibly. When Lucky finally slows his monologue, Didi grabs his hat, and Lucky falls silent. Pozzo goes onto trample the offending hat, and Lucky becomes so
weak that he falls if not supported by the others.