pressure of saturated water vopour $=P$

volume of saturated water vapour $=V$

By ideal gas equation, $P V=n R T$

Where $n=$ amount of substane

$R=$ universal gas constant

$T=$ absolute temperature

as it is compressed isothermally, $T=$ constant

$\therefore P V=$ constant

$\Rightarrow P_{2} V_{2}=P_{1} V_{1}$

given data: $P_{1}=P$ and $V_{1}=V$

$P_{2}=$ ? and $V_{2}=\frac{V_{1}}{2}=\frac{V}{2}$

$\therefore P_{2} V_{2}=P_{1} V_{1}$

$\Rightarrow P_{2}=\frac{P_{1} V_{1}}{V_{2}}=2 P \Rightarrow P_{2}=2 P$

The final pressure will be $2 P$