Keith - you're _using_ the fact that \$$\text{hom} : \mathcal{X} \nrightarrow \mathcal{X} \$$ is a \$$\mathcal{V}\$$-enriched profunctor, but this is not a fact we've proved yet: at least, not in the lectures or the puzzles. The point of Puzzle 197 is to _prove_ this fact, from scratch, by showing that \$$\text{hom} : \mathcal{X}^{\text{op}} \times \mathcal{X} \to \mathcal{V} \$$ is a \$$\mathcal{V}\$$-enriched functor. One has to actually prove this at some point, just as I proved in the lectures that the hom-functor of a category is really a functor.