Learn Dutch: Welk deel van de taart wil je hebben? - Which part of the cake do you want to have?

Deel means "part" or "portion". In the context of fractions, this is the exact question you would ask to find out if someone wants de helft (half), een derde (a third), or een kwart (a quarter) of the cake.

Why is it welk deel and not welke deel?

Deel is a het-word (het deel). When you put the question word "which" in front of a singular het-word, you must use welk. If it were a de-word like taart, you would use welke (for example, welke taart).

Could I just say "Welk deel van de taart wil je?" without adding hebben at the end?

Yes, you can! Just like in English ("Which part of the cake do you want?"), you can leave out hebben when the meaning is obvious from context. However, explicitly including hebben (to have) is very common in Dutch and completes the sentence nicely.

Why is hebben pushed all the way to the end of the sentence?

This is the standard Dutch word order when using modal verbs. Because wil (from willen, meaning to want) is the conjugated verb in this sentence, any extra verbs like the infinitive hebben are pushed to the very end of the clause.