$PV =n R T=\text { constant }$

$P _1 V_1= P _2 V_2$

$PV = P _{ A }( V / 8)$

$P _{ A }=8 P$

Adiabatic process, PV $\gamma=$ constant $\gamma$ for monoatomic gas is $\frac{5}{3}$.

$P _1 V _1^\gamma= P _2 V _2^\gamma$

$\frac{ P _{ B }}{ P }=\left(\frac{ V _1}{ V _2}\right)^\gamma=\left(\frac{ V }{ V / 8}\right)^{\frac{5}{3}}$

$P _{ B }=32 P$

$\frac{ P _{ B }}{ P _{ A }}=\frac{32 P }{8 P }=4$