Which verb does the adverbial phrase "for many days" modify in this sentence: "People remember most of what they have studied for many days."
It's ambiguous, without context, whether for many days is modifier in the clause headed by remember or studied.
The object of remember could be understood in either of the following ways:
People remember [most of what they have studied] for many days.
or
People remember [most of what they have studied for many days].