The answer is 10mL of Y.
X+2Y→XY2
You have 10mL of 1M X therefore the number of moles of X is given by:
Number of moles= (Volume x Molarity)/1000 = (10mL x 1M)/1000 = 1/100 = 0.01 moles
And you have twice as many moles of Y as X, therefore number of moles of Y = 0.02.
Also you have 2M Y so,
0.02 = (Volume x 2M)/1000 → 20 = Volume x 2 → Volume = 10mL.
This is assuming of course that all of X and Y are used up.