Here's how to balance the reaction of fluorine with sodium hydroxide:

Unbalanced Equation:

F₂ + NaOH → NaF + O₂ + H₂O

Balancing the Equation:

1. Balance Fluorine: There are 2 fluorine atoms on the left and only 1 on the right. Add a coefficient of 2 in front of NaF:

F₂ + NaOH → 2NaF + O₂ + H₂O

2. Balance Sodium: There is 1 sodium atom on the left and 2 on the right. Add a coefficient of 2 in front of NaOH:

F₂ + 2NaOH → 2NaF + O₂ + H₂O

3. Balance Oxygen: There are 2 oxygen atoms on the right and 3 on the left. Add a coefficient of ½ in front of O₂:

F₂ + 2NaOH → 2NaF + ½O₂ + H₂O

4. Multiply to Eliminate Fractions: To get whole number coefficients, multiply the entire equation by 2:

2F₂ + 4NaOH → 4NaF + O₂ + 2H₂O

Balanced Chemical Equation:

2F₂ + 4NaOH → 4NaF + O₂ + 2H₂O