
From the above diagram, we can write,
x+y+43d=d
x+y=4d
Initially, when there is no dielectric inserted between the plates the capacitance will be, C0=dϵ0A.
When the dielectric slab is inserted, we can assume there are 3 capacitors that are connected in series.
C1=xϵ0A, C2=3d4Kϵ0A and C3=yϵ0A
The equivalent capacitance,
C1=C11+C21+C31⇒C1=ϵ0A1(x+4K3d+y)⇒C1=ϵ0A1(4d+4K3d)⇒C=d(3+K)4ϵ0AK⇒C=3+K4KC0