Question

If the formula for a compound is represented by XY2 and the charge on the Y ion is -2, what is the charge in the X ion?

Answer 1

you have to multiply the charge of Y by the sub index of Y change the sign and divide by the sub index of X (in this case is 1 you can skip this step). That is going to be the charge of X.
If the XY2 compound were also an anion XY2- or a cation XY2+ you have to consider that charge also in your calculations (this is not your case now)