A parallel plate capacitor has two layers of dielectrics as shown in figure. This capacitor is connected across a battery, then the ratio of potential difference across the dielectric layers is

3/2

Capacitance (for k = 2)

$C_1=\frac{\varepsilon_0 kA}{d}$

$C_1$ = 2C   Where  C = $\frac{\varepsilon_0 A}{d}$

Capacitance (for k = 6)

$C_2 =\frac{6 \varepsilon_0 A}{2 d}$

$C_2$ = 3C

Therefore ratio of potential difference across the dielectric layer is = 3/2