Oxidation numbers of X, Y, Z are +6, -2 and -1 respectively. Possible molecular formula when atoms combine:

Explanation

A neutral compound must have oxidation numbers summing to zero, and XY2Z2 gives plus 6, then two at minus 2 and two at minus 1, that is 6 minus 4 minus 2, which is exactly zero. Testing each option the same way disposes of the others: XYZ2 gives 6 minus 2 minus 2, which is plus 2 rather than zero. Summing to zero is the only test needed for a neutral formula.