He is . . . . . . . . honourable man in the locality.

Answer: Option B

'A' and 'An' are indefinite articles and 'the' is the only definite article in the English language. 'The' is used with reference to something specific such as a specific person or place. This sentence does not talk about a specific honourable man, hence 'the' will not be used.
'A' cannot be used with honourable because it begins with a vowel sound. By rules of grammar, 'an' is used before a word that begin with vowels or vowel sounds. The word honourable begins with a vowel sound (o) because H is silent, similar to the pronunciation of 'hour.' Hence, Option B 'an' is correct.