Here is a picture of . . . . . . . . village where I was born. It is about ten minutes by . . . . . . . . car from Wellington, . . . . . . . . big town.

The noun 'village' is made specific by the words 'where I was born'. Hence we use the article 'the' and option B is wrong.
When the noun is spoken of in general sense, we omit the article. 'By car' is an expression that indicates the mode of travel. It does not talk about a car. Hence this blank won't require an article.
'Town' is a non-specific noun. The phrase 'a big town' describes 'Wellington' and is not specific on its own. Hence we use the article 'a'.