The <em>correct answer</em> is:
y-axis, x-axis, y-axis, x-axis
.
Explanation:
A reflection across the y-axis negates the x-coordinate; algebraically,
(x, y)→(-x, y).
A reflection across the x-axis negates the y-coordinate; algebraically, this takes our new point
(-x, y)→(-x, -y).
Reflecting again across the y-axis will take our new point
(-x, -y)→(x, -y).
Reflecting again across the x-axis will take our new point
(x, -y)→(x, y).
This is where we started; thus the polygon is mapped onto itself.