What set of reflections would carry rectangle abcd onto itself?
y-axis, x-axis, y-axis, x-axis
x-axis, y=x, y-axis, x-axis
x-axis, y-axis, x-axis
y=x, axis, x-axis

The set of reflections that would carry rectangle ABCD back to itself is:
y-axis, x-axis, y-axis, x-axis.

By reflecting the original image over y-axis, the transformed image moves to the 1st quadrant of the cartesian plane. By reflecting the image in quadtrant 1 over x-axis, the image moves to the 4th quadrant, and by reflecting it again over y-axis and another over the x-axis, it goes back to its original position in the 2nd quadrant.

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.