Learn Dutch: Hoe kunnen we hen beiden motiveren? - How can we motivate both of them?

You add the -n to beide when two conditions are met: it refers specifically to people, and it stands on its own as a pronoun rather than coming right before a noun. Here, beiden stands alone and refers to hen (them, meaning people), so it needs the -n. If it came before a noun, like beide studenten (both students), the -n would be dropped.

Why do we say hen beiden instead of translating "both of them" word-for-word?

Dutch does not use a literal translation like beide van hen for "both of them". Instead, you just put the object pronoun right before the word for "both". For example, hen beiden (them both), ons beiden (us both), or jullie beiden (you both).

Why is hen used here instead of hun or ze?

Hen is the direct object pronoun for "them" (referring to people). Because they are the ones receiving the action of being motivated, they are the direct object. You could also use ze, which is more common in everyday spoken Dutch, but hen is slightly more formal. You cannot use hun, because hun is only used for indirect objects (like "to them") or as a possessive ("their").

Why does the verb motiveren go at the very end of the sentence?