OPTION D is the correct answer.
There are two types of articles:
DEFINITE ARTICLE (THE) : Article 'the' is used to refer to a DEFINITE thing or person.
INDEFINITE ARTICLE(A/AN): Article 'a/an' is used to refer to a thing or person in general. For instance: man, door etc.
Article 'a' is used with consonant sounds whereas article 'an' is used with vowel sounds.
In the first blank, my is a possessive adjective, therefore, no article will be used.
In the second blank, month is a common noun, therefore, article a will be used.