Why "des pommes, des noix", but not "des lait" as well? Because the milk isn't plural?
"pommes" and "noix" are things you can count by numbers. "Lait" is not (uncountable: a certain quantity of)
So, in singular: une pomme,une noix, du lait; and in plural: des pommes, des noix, du lait.
Aha! Gotcha. Thanks for the reply.
Sometimes I can recognise that certain words like milk, wine and tea have du as the article but am hard put to know exactly why.
Your comments always improve the foundational skills of the people who read them.
Also note, du is not an article, but the partitive de plus the class le lait
Why are definite articles before the foods not listed as possible answers?
Because they are not an option here. In English, the meaning is "some apples, some walnuts, some milk".
Therefore, this is typically an indefinite case, where the French use the indefinite articles.
why is 'noix de cerneau' considered wrong?
"noix" is enough to translate "walnut" even if it also means the generic "nut" family.
"un cerneau de noix" (and not "une noix de cerneau") is "a walnut kernel", ie a half of a walnut (looking like a brain).