What is the correct preposition in the sentence: They walked ______ home after the game.

In the context of the sentence "They walked ______ home after the game," the correct preposition to use is "to." When referring to going to a person's home, the preposition "to" effectively indicates direction or destination. In this scenario, it signifies that the individuals are moving from one location (the game) to another (home). This is a common structure in English, where "walked to" illustrates the act of traveling toward a specific place.

The other prepositions do not accurately convey the intended meaning of the sentence. "At" suggests a location rather than direction, while "for" indicates purpose rather than movement. "With" implies companionship rather than destination. Therefore, "to" is the most appropriate choice as it correctly aligns with the action of traveling toward a known endpoint.