Show that $B(X,Y^*)$ and $B(Y,X^*)$ are isometrically isomorphic. 
If $X$ and $Y$ are normed spaces then we define. $$B(X,Y)= \{ f:X\rightarrow Y | f :\text{ f is a linear operator and bounded }\}$$
$X^*= \{f:X \rightarrow \mathbb{R}  | \text{ f is a linear operator and bounded }\}$

I only know Hanh-Banach Theorem. And I don't know how even start. Something that confuse me is how to send functions that send a vector in a linear functional in a function that send a vector in a functional.
This seems super hard. How should I think about this?

Given a bounded operator $T:X \to Y^{*}$ define $S: Y \to X^{*}$ by $(Sy)(x)=(Tx)(y)$. It is fairly routine to very that this is an isometric isomorphism. I will be glad to provide details if you get stuck. 
