To find the reaction order of an equation we need to check the exponents in the rate law's equation, and in this question the rate law's equation is given as:
Rate = k[ClO2]^x * [OH]^y
This x and y are the exponents which will give us the answer about the reaction order
In the experiments we see an increase of OH which represents a first-order reaction, and the decrease of ClO2 represents a second-order reaction, so the rate law's equation is:
Rate = k[ClO2]^2 * [OH]
Therefore ClO2 has a reaction order of 2