If the pressure and absolute temperature of 4 litres of ${\mathrm{SO}}_2$ gas are doubled, the volume of this gas would be 

For pressure $\mathrm{P}\propto \frac{1}{\mathrm{V}}$

When the pressure of the gas goes doubled then the volume gets half.

Now, the volume of the gas $\frac{4}{2}=2 \mathrm{litres}$

For temperature $\mathrm{T}\propto \mathrm{V}$

When the temperature of the gas goes doubled then the volume gets doubled.

Now the volume will be $2\times 2=4 \mathrm{litres}$

Hence, the volume remains unchanged.

The correct option is B.