The electric field on two sides of a charged non conducting plate is shown in figure. The charge density on the plate is given by

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 = $\frac{\sigma }{2{\epsilon }_0}=2$

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