I have a real issue with determining the centre of gravity for the y axis of an aircraft, especially with selecting the reference/datum point and how to measure the displacement. Please I would really appreciate any form of help I can get.
Transport airplanes have lateral C of G limits in terms of x distance from the centerline, but this only a certification requirement (related to roll authority in a critical case situation) and is only expressed for the flight crew as a fuel imbalance limit, fuel being the dominant factor, and is not accounted for in weight and balance data that the crew uses to determine if loading is correct.
The datum is the x=0 axis, with the C of G to the left, on, or right of it. To calculate it, you would need an empty lateral C of G position, determined by weighing the airplane and working out the empty C of G offset to left or right of the x axis based on the weight difference between the left and right main gear weighing points, and the distance of those points from x.
Then you can add fuel and passengers and calculate the change if any to the lateral C of G. Since the passengers are normally randomly distributed on the left and right side of the cabin, the passengers can normally be considered neutral. Then it's only the effect of an unequal fuel load.
But as I said, for practical purposes, the fuel imbalance limits in the airplane's operating limitations account for the requirement to stay within maximum lateral C of G limits, and it's not necessary to calculate it.