A determiner is 'a modifying word that determines the kind of reference a noun or noun group has, for example a, the, every.'
Option B: For the given sentence, 'a few' is the most suitable option. 'A' and 'few' are both determiners. 'A' is an article that modifies the noun 'years' and 'few' tells us a non-definite number that means 'a small number of'.
Hence option B is correct.
Option A: 'Much' refers to a singular, uncountable noun, 'We don't have much milk.' The noun here, 'years' is plural and countable.
Option C: The article 'a' isn't present here. Without the article, the sentence sounds incomplete.
(Also, 'few' on its own means 'not many' whereas 'a few' means 'a small number'. The former is a negative meaning and the latter focuses on the number.)
Option D: 'Any' is used in negative statements, or in questions. It does not agree to the sentence.
Hence options A, C and D are incorrect.