From the figure it is cleared that the plate in an external field. Let the electric field due to plate is E and $E_o$ be the external field
$E_o$ + E = 12
$E_o$- E = 8
Electric field due to plate = $\frac{\sigma }{2{\epsilon }_0}=2$

                                    $\Rightarrow \sigma =4{\epsilon }_0$