b
As gas is suddenly compressed, the processes is adiabatic.
Equation of gas for adiabatic process is
$PV ^\gamma=\text { constant. }$
$\Rightarrow P _1 V _1^\gamma= P _2 V _2^\gamma$
$\Rightarrow P _0 V _0^\gamma= P _2\left(\frac{ V _0}{4}\right)^\gamma$
$\Rightarrow P _2= P _0(4)^\gamma$