The poisonous gas hydrogen sulfide, H2S, can be neutralized with a base such as sodium hydroxide, NaOH. The unbalanced equation for this reaction follows:
NaOH(aq) + H25(e) → Na2S(aq) + H2O(1)
A student who was asked to balance this equation wrote the following:
Na2OH(aq) + H2S(g) → Na2S(aq) + H2O(
Is this equation balanced? Is it correct? Explain why or why not, and supply the correct balanced
equation if necessary.

It's not correct. For balancing, we need to put the coefficients in the molecule, not in the athom. Because if you do this, you're creating another molecule, instead of a balacing, for which the reaction may not happen - but anyway, it would be another reaction.

The correct balacing is:

2NaOH + 1H2S → 1Na2S + 2H2O

Explanation:

Look: Na2OH does not even exist. OH has only one free link, so he can't - in normal conditions - make another one with any athom. That's why we should write 2NaOH instead of Na2OH. The first means "2 mols of NaOH".