'Any' is generally used to refer to an indefinite quantity of something in interrogative or negative sentences. As the sentence in question is neither interrogative nor negative, option B is an incorrect answer.
'Little' implies a small quantity. Since from the sentence, we don't know for sure if it was only a small quantity of coffee offered, option C is not an appropriate answer.
We use 'much' in questions and negative clauses to talk about the degree of something. As we are clearly dealing with the quantity of coffee offered and not the degree of anything, option D is incorrect.