Learn Dutch: Begrijpen jullie hen niet? - Do you not understand them?

You can actually use either! Hen is used specifically for people and is a bit more emphasized or formal. Ze is the everyday, unstressed version and can be used for both people and things.

Is jullie a subject pronoun or an object pronoun here?

In this sentence, jullie is the subject (the people doing the understanding). However, jullie is also the object pronoun for "you" (plural). The word stays exactly the same whether they are doing the action or receiving it!

Why does the sentence start with the verb Begrijpen?

Because this is a yes/no question. Just like in earlier lessons, to turn a statement like Jullie begrijpen (You understand) into a question, you swap the verb and the subject to make Begrijpen jullie (Do you understand).

Why is niet at the very end of the sentence?

When you negate an action that involves a specific object (like a pronoun such as hen), the word niet is placed after that object.