Answer
When the switch is closed, the potential difference across capacitor 2 is reduced, so $10.8~\mu C$ of charge moves from capacitor 2 to capacitor 4.
Work Step by Step
When the switch is closed, $7.20~\mu C$ moves through point P from the battery to capacitor 1.
Then in turn $7.20~\mu C$ moves from capacitor 1 to capacitor 4.
However, when the switch is closed, the potential difference across capacitor 2 is reduced, so $10.8~\mu C$ of charge moves from capacitor 2 to capacitor 4.
The total charge that ends up on capacitor 4 is $18.0~\mu C$
