To find the value of X^2 / Y^2, we need to simplify the given equation and then substitute the values of X and Y.

Given: X + 2Y = 2X + Y

Let`s simplify the equation:

X + 2Y = 2X + Y

X - 2X = Y - 2Y

-X = -Y

Now, let`s square both sides of the equation:

(-X)^2 = (-Y)^2

X^2 = Y^2

Since X^2 is equal to Y^2, we can conclude that X^2 / Y^2 is equal to:

X^2 / Y^2 = Y^2 / Y^2 (substituting X^2 = Y^2)

X^2 / Y^2 = 1

Therefore, X^2 / Y^2 is equal to 1.