How much charge flows through switch $S$ when it is closed?

Initially,

$q=C_{\text{net }}V$

   $=\left(2\mu \mathrm{F}\right)$

    $=36\mu \mathrm{C}$

Finally,

$q_1=72\mu \mathrm{C}$

$\Rightarrow q_2=18\mu \mathrm{C}$

Charge flow from $S=\left(\text{Final charge on plates }p\text{ and }r\right)-\left(\text{Initial charges on plates }p\text{ and }r\right)$

                             $=(-72+18)-(-36+36)$

                             $=-54\mu \text{C}$