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 [ClO2] 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.