This is a stoichiometry problem, where we want to know how much of the reactant is needed to produce a certain amount of product, in order to do that we need to:
1. Set up the properly balanced equation, which the question already provided us
2. See how many moles of product we have, which is 88 moles of O2
3. Check the molar ratio between the two compounds, which we can see by the balanced equation that the molar ratio is 2:3, which means that for every 2 moles of NaClO3, we will end up with 3 moles of O2
Now we can do our calculation
2 NaClO3 = 3 O2
x NaClO3 = 88 O2
x = 58.6 moles of NaClO3, rounding to the nearest whole number will be 59 moles of NaClO3