Sort of. You need to evaluate $\displaystyle \begin{align*} \frac{\partial ^2 \phi}{\partial t^2} \end{align*}$ and $\displaystyle \begin{align*} \frac{\partial ^2 \phi}{\partial x^2} \end{align*}$ and show they're equal, which is what you have tried to do. But you just need to set it out better. Also you can't use Newton's notation " ' " for a derivative here, because these are partial derivatives...