The balanced chemical reaction you provided is:
\[ 2H_2 + O_2 \rightarrow 2H_2O \]
In this reaction, the left side shows 4 hydrogen atoms (from \(2H_2\), which is 2 molecules of \(H_2\), and each \(H_2\) has 2 hydrogen atoms).
On the right side, in the products \(2H_2O\), there are also 4 hydrogen atoms (since each \(H_2O\) has 2 hydrogen atoms, and there are 2 molecules of \(H_2O\)).
Therefore, the total number of hydrogen atoms present after the reaction remains 4.
So, the correct answer is 4.