Change into Passive Voice:

The boy laughed at the beggar.

The correct option is (D)

The beggar was laughed at by the boy.
Given sentence is in Past indefinite (Past simple) tense and it is in the active voice. To change it into Passive voice Object (the boy) will become the subject and the subject (The beggar) will be the object. We also use the helping verb of past simple tense was with the V3 form of the main verb. Keep in mind that the preposition at must be retained with the verb.

Rule :
Subject + (was /were) + V3 + Other Agents.