In order to balance a chemical equation, we need to have equal numbers of each type of atom on both sides of the equation. To determine the coefficient for O2 in the reaction above, we need to look at the number of oxygen atoms present in each compound.

On the left side of the equation, we have y moles of O2, which contain 2y oxygen atoms. On the right side of the equation, we have z moles of AS2O3, which contain 3z oxygen atoms.

To balance the equation, the number of oxygen atoms on both sides must be equal. Therefore, we need to find the value of y that satisfies the equation 2y = 3z.

Looking at the given options, we can calculate 2 times each option and check if it is divisible by 3 to find a value of z.

2 * 5 = 10 (not divisible by 3)

2 * 7 = 14 (not divisible by 3)

2 * 9 = 18 (divisible by 3)

2 * 11 = 22 (not divisible by 3)

Therefore, the only value of y that makes the equation balanced is 9, as 2 * 9 = 18