"Darunter hat der Koch manche Äpfel."
Duolingo often translates "some" as "manche". But this is uncommon. Depending weakly on the number of apples you could say "ein paar Äpfel" (few but more than two), "einige Äpfel" (maybe 3-10), "mehrere Äpfel" (more than one) "viele Äpfel" (roughly more than 10) or simply "Äpfel". The last being the closest translation of "some apples" in my opinion.
"Manche" is not used to depict an amount, but "manche" actually can be used with "Äpfel" though: "manche Äpfel sind schlecht" = "some apples are rotten". The use of "manche" here means that there are others that are still good. This is mostly the case with "manche", it tells you that there are others too. "Manche Leute mögen einfach keinen Jazz."
Aside from that "some" is often necessary in English but mainly just omitted in German.
As an aside, "the cook has apples under there" sounds also right to my uneducated ears, but I would think you would only say this a context where apples are unexpected, like: "Gosh, the cook has apples under there!" Or "I thought he'd offer pears, but the cook has apples under there!" English speakers please, can you confirm?