To solve this problem, let's analyze each transformation option and check whether it carries the rectangle onto itself.

Step-by-step analysis:

1. Reflection over the line $y = 0$ (x-axis):

   • Reflecting over the x-axis would flip the rectangle vertically.
   • Since the rectangle is symmetric above and below the x-axis, this reflection does carry the rectangle onto itself.

2. Reflection over the line $x = -3$:

   • This line passes through $x = -3$, a vertical line.
   • The rectangle is not symmetric with respect to this line because it lies across different x-values.
   • Therefore, this transformation does not carry the rectangle onto itself.

3. Rotation of $180^\circ$ counterclockwise about the origin:

   • Rotating $180^\circ$ flips the rectangle around the origin.
   • Since the rectangle is symmetric about both axes (centered at the origin), this transformation carries the rectangle onto itself.

4. Reflection over the $y$-axis:

   • Reflecting over the y-axis flips the rectangle horizontally.
   • Because the rectangle is symmetric about the y-axis, this transformation does carry the rectangle onto itself.

Conclusion:

The transformation that does not carry the rectangle onto itself is:
"a reflection over the line $x = -3$."

Would you like further clarification on symmetry or transformations? Let me know!

Related Questions:

1. What is symmetry in geometric shapes, and how is it identified?
2. How does reflection over the x-axis affect the coordinates of a shape?
3. What happens to a shape's coordinates when rotated $180^\circ$ about the origin?
4. How do you test whether a shape is symmetric about a line?
5. What are real-world examples of transformations like reflections or rotations?

Tip: Symmetry about a line means the shape looks identical on both sides of the line after folding. Always check for this property in geometric transformations.