Consider the network shown below: 

 

 

 

 

 

 

 

 

On closing the switch, the charge flown through the switch is

Before closing : 
  
  $C_{eff}=\frac{\frac{2\times 4\times 8}{4+8}\times 6}{\frac{2\times 4\times 8}{4+8}+6}$ $=\frac{32}{\frac{16}{3}+6}$   
 $=\frac{96}{34}=\frac{48}{17}\mu F$     $\Rightarrow Q_{battery}=CV=48\mu C$    
 After closing the swithch : 
 

 $C_{eff}=\frac{6\times 6}{6+6}=3\mu F$ 
 $\Rightarrow Q=51\mu C$ 
$\Rightarrow$ Charge through switch =
$(34-17)-0=17\mu C$