Answer:
Stoop
Step-by-step explanation:
In the poem, the Duke is showing a painting of his late wife, the Duchess, to a visitor. He describes her as being beautiful and accomplished, but also as being too easily impressed and too quick to smile. He says that he "gave commands" and "then all smiles stopped together". This suggests that he killed her for being too independent and for not showing him the respect he believed he deserved.
The Duke's refusal to "stoop" is a metaphor for his refusal to compromise or to be anything less than absolute authority. He is a controlling and possessive man who believes that women are objects to be owned and controlled. He will not "stoop" to discuss his wife's behavior with the visitor, because he does not believe that he has to explain himself to anyone.
The other options are incorrect. The Duke does show the painting to the visitor, and he does eventually remarry. However, he does so on his own terms, and he will not compromise his authority for anyone.