Given that |x|=|y|

Now, |x| = |y| means that the Absolute value of x and y is same. There are multiple cases possible. Let's understand this using values

Case 1: x +ve, y +ve. Ex: x = 2, y = 2. Making |x| = |y| = |2| = 2
Case 2: x +ve, y- ve. Ex: x = 2, y = -2. Making |x| = |y| = |2|= |-2| = 2
Case 3: x -ve, y +ve. Ex: x = -2, y = 2. Making |x| = |y| = |-2| = |2| = 2
Case 4: x -ve, y- ve. Ex: x = -2, y = -2. Making |x| = |y| = |-2|= |-2| = 2

Now, in all of these cases if we square x and y then we will always have \(x^2\) = \(y^2\)
So, any even power of x and y will always be equal

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Absolute Values