The correct answer is: D. no article
Eggs are sold by the dozen. This means that a dozen eggs are sold as a unit. The word "dozen" is a collective noun, which means that it refers to a group of things as a whole. In this case, the group of things is eggs.
The other options are incorrect because they are all articles. Articles are words that are used to introduce nouns. In this case, the noun is "eggs." The articles "a" and "an" are used before singular nouns, while the article "the" is used before specific nouns. In this case, the noun "eggs" is not singular or specific, so no article is needed.