In Act four scene 3 King Claudius learns of Polonius's death. Remember that in the previous scene young Hamlet stabbed Ophelia's father through a tapestry thinking it to be Claudius spying on him.
Hamlet should be punished for the murder, but Claudius is very cautious to punish the young prince. He knows that Hamlet is very popular with the people of Denmark, and so to publicly punish him could be detrimental to his approval rating with his people.
Yet must not we put the strong law on him.
He's loved of the distracted multitude,
Who like not in their judgment, but their eyes;
Instead, he decides on a secret plan to send Hamlet to England with letters urging England to punish him since he cannot. The punishment he plans for his son/ nephew is death.