How to convert cell diagram to a chemical equation?
Assuming you meant $\ce{MnO^-4}$ and not $\ce{MnO^{4-}}$, your reduction half reaction is incorrect. Because according to your equation $\ce{Mn^{2+}}$ is being oxidised to $\ce{MnO^-4}$ rather than being reduced.
The correct half cell reactions would be:
$$
\ce{Zn -&gt; Zn^{2+} + 2e-}\\
\ce{MnO^-4 + 8H+ + 5e- -&gt; Mn^{2+} + 4H2O}\\
$$
And so the overall balanced reaction would come out to be:
$$\ce{5Zn + 2MnO^-4 + 16H+ -&gt; 5Zn^{2+} + 2Mn^{2+} + 8H2O}$$