Final answer:
The question seeks to identify an important matter that Danglars wanted to discuss with his wife after politely sending Debray out of his house. The provided excerpts do not contain details about this specific matter.
Step-by-step explanation:
Married to the Baron Danglars, Hermine Danglars once had an affair with Villefort that resulted in the birth of a child, Benedetto. The day after Danglars leaves, Madame Danglars rushes to Lucien Debray in a panic. She shows him the letter Danglars has left explaining his reason for running away. He has written that a series of strange events has left him bankrupt and unable to repay the debt to the hospital.
The specific scene in a literary work where Danglars subtly forces Debray to leave his house to discuss an important matter with his wife. The precise topic or important matter that Danglars wishes to discuss with his wife is not provided in the provided excerpts. However, based on these excerpts, the scene involves interpersonal relationships and possibly confidential matters being discussed after ensuring privacy by dismissing another character.