Learn Dutch: Wie had jouw scriptie eigenlijk moeten begeleiden? - Who should have supervised your thesis actually?

This is a classic example of the IPP effect (Infinitivus Pro Participio). When a modal verb like moeten is used with another verb in a perfect tense, Dutch swaps the expected past participle for the infinitive. So instead of using gemoeten, you get two infinitives at the end of the sentence: moeten begeleiden.

How do we express the idea of "should have" in Dutch?

To express an unfulfilled past obligation like "should have supervised", Dutch uses the past tense of hebben combined with moeten and the main verb. In this sentence, had ... moeten begeleiden literally translates to something like "had must supervise".

Why is the word order moeten begeleiden and not begeleiden moeten at the end?

When you have a cluster of infinitives at the end of a sentence due to the IPP rule, the modal verb (moeten) almost always comes before the main action verb (begeleiden).

What nuance does the word eigenlijk add to this question?

Eigenlijk translates to "actually" or "in reality". In sentences about unfulfilled obligations, it emphasizes the contrast between what was supposed to happen and what really happened, making the question sound more natural and conversational.