How do you define a right coadjoint action?

Question

The left coadjoint action of a finite-dimensional Hopf algebra $H$ on $H^{*}$ is $\sum\phi_{(2)}\langle h, (S\phi_{(1)})\phi_{(3)}\rangle$, where $h\in H$ and $\phi\in H^{*}$. How do you define a right coadjoint action of $H$ on $H^{*}$?