The given sentence is in the active voice, as the subject 'The peon' performs an action 'refused' against the object 'him'.
If this sentence is changed to passive voice, then the subject is also changed, in order to retain the meaning of the sentence.
So,
the object takes the place of the subject and vice versa and the word
'by' is introduced as now the subject receives the action by the object.
The verb form of the sentence is also changed from active form to
passive.
'Subject (The peon) + verb (refused) + indirect object (him) + direct object (admittance)' changes to:
'New subject (He) + verb (was refused) + direct object (admittance) + by + new object (the peon)'
The
passive form of 'refused' in the simple past tense is 'was/were refused'.
This can be seen in option A, hence it's the right answer.
Option B: The verb 'is' expresses the simple present tense whereas the sentence is in the past 'refused'.
Option C: The given sentence has two possible passive forms, as there are two
objects: indirect object (him) and direct object (admittance). When the direct object 'admittance' is made the subject, then the indirect object
'him' follows the verb. The new object 'by the peon' should come last, and
shouldn't be followed by the indirect object 'him'.
So, this option does not have the correct passive form.
Option
D: The preposition 'to' is missing. Since the indirect object 'him' comes after the direct object 'admittance', the word 'to' is essential.
Hence options B, C and D are incorrect.