Two large, thin metal plates are parallel and close to each other. on their inner faces, the plates have surface charge densities of opposite signs and of magnitude $16\times {10}^{-22} C m^{-2}$ The electric field between the plates is

Here, Consider a surface above any plate of area A, 

The total electric flux through this area will be $\varphi =E.A$, where $E$ is the electric field.

By using gauss theorem,

$\varphi =\frac{Q}{{\epsilon }_o}$, as the plates are uniformly charged

$Q=A.\sigma , where \sigma =16\times {10}^{-22} C m^{-2}$

$\Rightarrow$ $E = \frac{\sigma }{{\epsilon }_0} =\frac{16\times {10}^{-22}}{8.854\times {10}^{-12}}$

            $=1.8\times {10}^{-10} N C^{-1}$