While converting to indirect speech (IDS), the verbs in DS are changed from simple present tense into simple past tense. Hence, the verb, 'do not/ don't' in DS is changed to 'did not/ didnt' in IDS. The pronouns in the DS are changed to represent the relation with the reporter and not the speaker. So, the pronouns 'you' and 'your' in DS are changed to 'he' and 'his' in IDS. The male pronouns ('he' and 'his') are used because the person being addressed (Mr.Ghost) is a male. The positions of the subject (he) and verb (did not) are inverted in IDS. So instead of saying, 'didn't he', we say, 'he didn't' in IDS.
The complete sentence in IDS is: 'Mr.Otis asked Mr.Ghost why he didn't oil his rusty chains'. Hence, option A is correct.
Option B: In IDS, the positions of the subject and verb are inverted. Hence, 'didn't he' has to be used instead of 'he didn't. However, the positions are not not changed in option B and hence it is incorrect.
Option C: The verb 'did not' has been changed to 'had not' in option C. This is incorrect.
Option D: In IDS, the past tense form of the verb has to be used. In option D, the verb, 'does' is in present tense. Hence, this is incorrect.