"The princess is the king's daughter."
Translation:Die Prinzessin ist die Tochter des Königs.
"Die Prinzessin ist des Königs Tochter."
Should be an accepted answer as it works perfectly fine in German and, with all respect, is an even more direct translation than Duolingo's suggestion.
- the king's daugher = des Königs Tochter / die Königstochter
- the daugher of the king = die Tochter des Königs
I think the definiteness of ‘daughter’ in this case is debatable, since a genitive or possessive generally makes a noun at least somewhat definite (take, for example, how you can't use the indefinite article with genitive or possessive pronouns and you have to reword the sentence, like ‘a daughter of the king’, ‘one of the king's daughters’, ‘a friend of mine’, ‘one of my friends’). Aside from this, even if the king had more than one daughter, I believe you could still say ‘sie ist die Tochter des Königs’, ‘sie ist eine Tochter des Königs’ puts much more stress on the indefiniteness, closer to ‘one of the daughters of the king’.