I do not follow in the sinppet below how from the fact that $({\cal K},\otimes,I)$ is a symmetric monoidal closed category follows that the functor $$[-,D]:\cal K\to K^{op}$$ has domain $\cal K$ and codomain $\cal K^{op}$ ? Perhaps I would also need to recall the definition of a symmetric monoidal closed category. I understand that $[X,D]$ is the set of all functors from $X$ to $D$.
