In order to balance an equation, you need to add coefficients in order to make the number of atoms on each side equal. That's a little technical, so let me explain. In H2+O2 --> H2O, on the left, we have 2 hydrogen atoms and 2 oxygen atoms. On the right, we have 2 hydrogen atoms and 1 oxygen atoms.
Now, we can multiply each "term," so to speak, in order to balance the equation. We need the same amount of atoms on each side. So, we can multiply H2, O2, and/or H2O by any amount in order to make the amount of hydrogen atoms and oxygen atoms, on both sides, equal. When we multiply each term, we are adding more molecules. For example, if we multiply H2 by 2 (written as 2H2), there are now 2 H2 molecules on one side of the expression.
So, back to our statement: H2+O2 --> H2O. Let's multiply H2O by 2 (double the amount of water molecules): H2+O2 --> 2H2O. Now, we have to multiply the coefficients together, like using the distributive property. 2H2O = 2(H2+O) = (2*H2)+(2*O) = 4 hydrogen and 2 oxygen atoms. On the left, we still have 2 hydrogen atoms and 2 oxygen atoms.
So, our oxygen atoms are equal. 2=2. We don't have to do anything about that. However, on the left, we only have 2 hydrogen atoms; on the right, we have 4. How do we fix this? Multiply the H2 molecule on the left by 2! As we calculated earlier, 2*H2= 4 hydrogen atoms.
So, let's check. Our statement would be 2H2+O2=2H2O. Multiply the coefficients: 2*H2 = 4 hydrogen atoms. O2 is 2 oxygen atoms. On the other side, we again have 2*H2 = 4 hydrogen atoms, and 2*O = 2 oxygen atoms. 4=4, and 2=2. Our equation is balanced!
Answer: 2H2+O2=2H2O
