alevel chem rates of reaction help

The reaction is first order with respect to compound X and second order with respect to compound Y. By what factor will the rate increase if the concentrations of X and Y are both doubled?

It says the answer is 8, but why is this? If someone could talk me through this it would be great thx

If you double X it increases the rate by a factor of 2.
If you double Y it increases the rate by a factor of 4
If you double both the rate increases by a factor of 2 x 4 = 8