Answer
The capacitance is $~~17.4\times 10^{-12}~F$
Work Step by Step
We can find the capacitance of the bottom half of the capacitor:
$C = \frac{\kappa_1~\epsilon_0~A}{d/2}$
$C = \frac{(11.0)(8.854\times 10^{-12}~F/m)(7.89\times 10^{-4}~m^2)}{2.31\times 10^{-3}~m}$
$C = 33.266\times 10^{-12}~F$
We can find the capacitance of the top half of the capacitor:
$C = \frac{\kappa_2~\epsilon_0~A}{d/2}$
$C = \frac{(12.0)(8.854\times 10^{-12}~F/m)(7.89\times 10^{-4}~m^2)}{2.31\times 10^{-3}~m}$
$C = 36.290\times 10^{-12}~F$
Note that the two layers are in series.
We can find the equivalent capacitance:
$\frac{1}{C_{eq}} = \frac{1}{33.266\times 10^{-12}~F}+\frac{1}{36.290\times 10^{-12}~F}$
$C_{eq} = 17.4\times 10^{-12}~F$
The capacitance is $~~17.4\times 10^{-12}~F$
