How can you tell the matter is conserved in this reaction?

Answer:
You basically look at it. Count up the atoms in the graphic or the equation below it.
Explanation:
You probably should've asked in the chemistry thread (though this is kind of like very basic biochemistry).
Left side: 2H₂O₂ means there should be a total of 4 hydrogen and 4 oxygen on both sides of the reaction.
Right side: 2H₂O means there are 4 hydrogen and 2 oxygen. Does that mean matter was not conserved? No! The right side also shows an additional O₂, which totals up to a grand 4 hydrogen and 4 oxygen on the right side.
As you can see, if all of the atoms are present in a balanced equation, you say matter is conserved.