Following is the step by step method of Balancing of the reaction
First, balance Br atoms. So on the RHS you get
Br2 + H2 O2 ====> 2 Br O2 + H2 O
Now let n be num of molecules of H2O2.
Br2 + n H2 O2 ==> 2 Br O2 + x H2O
2n H atoms on left and 2 x H atoms on right => n = x
now 2n atoms of O on LHS. 4 + n on right side.
=> 2n = 4 + n => n = 4
Br2 + 4 H2 O2 ==> 2 Br O2 + 4 H2O