There are 4 hydrogens on the right side [tex](2\mathrm H_2=4\mathrm H)[/tex], and 2 hydrogens on the left per molecule of [tex]\mathrm H_2[/tex]. To get the same number of hydrogens on both sides, the coefficient should be 2.
(Then the number of oxygens will be consistent, since [tex]2\mathrm H_2\mathrm O[/tex] contributes 2 oxygens, and so does [tex]\mathrm O_2[/tex].)
