In the passive voice, the object becomes the subject of the sentence, and the action is done to it. In this case, "the bucket" is the object, and we need to convey that it was filled by someone. The passive voice construction is "was/were + past participle."

Option (4), "The bucket was filled with hot water by the old man," correctly restructures the sentence into the passive voice, with "the bucket" as the subject and "was filled" as the passive verb construction, indicating that the bucket was the receiver of the action performed by "the old man." This choice follows the standard rules for transforming an active sentence into the passive voice.