David picked up . . . . . . . . nut from . . . . . . . . hole.

David picked up a nut from the hole.

"A" is used before "nut" because it refers to one nut among many, and it is being mentioned for the first time. The indefinite article is used to introduce something that is not specific or previously known.

"The" is used before "hole" because it refers to a specific hole from which the nut was picked. The definite article is used when the noun is specific or already known to the speaker and listener.

Option A: the, the is incorrect because "nut" is not specific initially, and we need the indefinite article "a".

Option B: a, an is incorrect because "hole" is specific, and we need the definite article "the", not "an".

Option D: the, a is incorrect because "nut" is not specific at first, and "hole" is specific, so it requires "the".

Conclusion: The correct answer is Option C: a, the, as it follows the correct usage of the indefinite article for a general noun and the definite article for a specific noun.