Choose the correct answer. It was a very difficult year for families.

The sentence requires a determiner that can be used with a plural countable noun like 'families'. 'A lot of' is the most appropriate choice here to indicate a large quantity. The phrase 'a lot of families' fits grammatically and semantically. The other options, 'any', 'lot of', and 'much', are not suitable in this context. 'Any' is typically used in negative or interrogative sentences. 'Lot of' is grammatically incomplete without 'a'. 'Much' is used with uncountable nouns. Therefore, the correct answer is a lot of.