Choose the correct sentence in passive voice.
Will the man carry the box to the room?

The sentence is in active voice where the verb expresses the action of subject upon object.
Thus to convert it into passive voice: Object + Helping Verb + Verb 3rd Form + By + Subject
The tense is simple future
so the rule is:
Active voice: Subject + Will/Shall + V1 + Object
Passive Voice: Object + Will/Shall + Be + V3 + By + Subject
Thus option 2 is the correct answer.