A parallel plate capacitor with square plates is filled with four...

${C}_{1}$ and ${C}_{2}$ are in series.

The equivalent capacitance of ${C}_{1}$ and ${C}_{2}$ is

${C}_{12} = \dfrac{{\in}_{0}\dfrac{A}{2}}{\dfrac{d}{2{K}_{1}} + \dfrac{d}{2{K}_{2}}} = \dfrac{{\in}_{0}A}{d}\dfrac{{K}_{1}{K}_{2}}{{K}_{1} + {K}_{2}}$

${C}_{3}\text{and}{C}_{4}\text{are in series}$

${C}_{34} = \dfrac{{\in}_{0}\dfrac{A}{2}}{\dfrac{d}{2{K}_{3}} + \dfrac{d}{2{K}_{4}}} = \dfrac{{\in}_{0}A}{d}\dfrac{{K}_{3}{K}_{4}}{{K}_{3} + {K}_{4}}$

${C}_{eq} = {C}_{12} + {C}_{34} = \dfrac{{\in}_{0}A}{d}\left(\dfrac{{K}_{1}{K}_{2}}{{K}_{1} + {K}_{2}} + \dfrac{{K}_{3}{K}_{4}}{{K}_{3} + {K}_{4}}\right)$

$∴ {K}_{eq} = \left(\dfrac{{K}_{1}{K}_{2}}{{K}_{1} + {K}_{2}} + \dfrac{{K}_{3} . {K}_{4}}{{K}_{3} + {K}_{4}}\right)$