A parallel plate capacitor with square plates is filled with four dielectrics of constants $K_1, K_2, K_3, K_4$ arranged in a $2 \times 2$ grid (left-right half and top-bottom half). The effective dielectric constant $K$ is:
The four dielectrics fill four quadrants. Each half of the plate area (left and right halves, each of width $d/2$) acts as two capacitors in series (top and bottom dielectrics), and these two series combinations are in parallel.
More directly using the standard result for this arrangement:
$K_{eff} = \frac{(K_1+K_2)(K_3+K_4)}{K_1+K_2+K_3+K_4}$
This comes from treating left column ($K_1, K_3$ in series) in parallel with right column ($K_2, K_4$ in series), where each column occupies half the area and full thickness $d$, but each dielectric occupies half the thickness $d/2$.
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