Consider two containers A and B containing monoatomic gases at the...

In an isothermal process the temperature is constant.

$PV = nRT$

So, it can be written that

$PV = {P}_{A}\left(\dfrac{V}{8}\right) ⇒ {P}_{A} = 8P$

In an adiabatic process,

$P{V}^{\gamma} =$constant

$\gamma$ for monoatomic gas is $\dfrac{5}{3}$

So, it can be written

$\dfrac{{P}_{B}}{P} = \left(\dfrac{V}{\dfrac{V}{8}}\right)\dfrac{5}{3} ⇒ {P}_{B} = 32P$

Thus, the ratio of the pressures is

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