Hello!
I will take a stab at answering this question.
I tried to go about this problem by thinking about the concentration of gas in each flask before and after the valve is opened. Initially, Region I has all X, Y, Z moles of Helium, Argon and Nitrogen in a certain volume V. When the valve is opened, we know that the gas will naturally want to move into Region II until an equilibrium is reached. But what is true at this equilibrium point? The concentration of gases in each vessel should be the same at equilibrium, so there is no net movement of gas in either direction. Therefore, given that there is three times more volume in Region II, there should be three times more moles of gas in Region II (corresponding to D).
n/V = 3n/3V
Another way to think of this problem is in terms of pressure. At equilibrium, both flasks should be at the same pressure so there is no net movement of gas into one container or the other.
Both vessels will be at the same pressure and temperature at equilibrium. Using the equation PV = nRT, if we increase V by 3, the number of moles n has to also increase by 3 since all other variables are constant.
I hope this helps.