How do you balance #HBr + O_2 -> Br_2 + H_2O#?
Add molecules (balancing numbers in front) to ensure that the number of atoms of each element is the same on the left and right hand sides of the equation.
This equation is one of those where you need to balance O at the very beginning.
Otherwise as a thumb-rule one leaves H and O to taken up at the last.
Observe that in the unbalanced equation, on the reactants side there are 2 atoms of oxygen, whereas there is single oxygen atom on the products side.
Therefore to balance O on both sides, we need to put 2 in front of water molecule. This fixes 4 hydrogen atoms on the right side of the equation.
To balance 4H atoms in the products, we need 4 molecules HBr on the reactants side.
Now we are left with balancing of bromine atoms. Clearly to balance 4 Br atoms on the reactants side, we need to put 2 in front of