3(gained 10 electrons)

 2(+5)=+10                                                   2(0)=0  
2H2O+10MnO2+2ClO3¯ → 3Cl2+ 10MnO4¯ +4H+
2(+3)                                                                                                                                                                 2(0)  

10(lost 3 electrons)       
 

1st: Balance all atoms with the exception of Hydrogen and Oxygen.

next step