Final answer:
Claudius did not retaliate against Hamlet for two reasons: his love for Gertrude and Hamlet's popularity with the common people which made it politically difficult for Claudius to act against him.
Step-by-step explanation:
The question pertains to William Shakespeare's play Hamlet, specifically a conversation involving the characters Claudius and Laertes in which Claudius provides his reasons for not retaliating against Hamlet for his treachery. Claudius cites one reason as his love and devotion to Gertrude, Hamlet's mother and Claudius' wife. The second reason Claudius offers is his concern for Hamlet's public image and the affection that the common people have for Hamlet. This popularity makes it politically difficult for Claudius to take direct action against him.