Final answer:
The sentence "Stagecoach stations along the way gave traveling passengers a chance to rest and eat." contains a compound direct object.
Step-by-step explanation:
The sentence "Stagecoach stations along the way gave traveling passengers a chance to rest and eat." contains a compound direct object. In this sentence, the compound direct object is "traveling passengers" and "a chance to rest and eat." The verb "gave" is being performed on both direct objects.