You don't have calculate of for X. You are given the values of X and Y here in the question.

X and Y are the concentrations of [ClO_{2}] and [OH] respectively.

Form equations with the data given and solve.

I am forming one for you.

Rate = k[X]^{m}[Y]^{n}

0.18 = k[0.10]^{m}[0.10]^{n}

Now make equations like this and solve for m, n and k.