The Order of Reaction is defined as, "the sum of the exponents of the concentration terms in the rate expression of the reaction".
The rate expression given is,
Rate = k [L]² [XY]
So,
The sum of exponents is,
2 + 1 = 3
It is a third order reaction, provided it is second order with respect to concentration of L and first order with respect to concentration of XY.
Result:
It is 3rd Order Reaction.