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Answer:
reflection across the angle bisector
Step-by-step explanation:
The arms holding the flags make an angle. If the bisector of that angle is used as a line of reflection, the left flag will be reflected to the position of the right flag.
A simple transformation to map the left flag to the right flag is ...
reflection across the angle bisector
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Additional comment
The left flag lies clockwise from the arm holding it. The right flag lies counterclockwise. To change that orientation, a transformation must be used that involves reflection. One way the transformation could be done is to reflect the left flag across the y-axis (vertical line through the center of the body), then rotate it CCW by an appropriate angle (45°, perhaps).
You could also rotate the flag 135° CCW and then reflect it across the horizontal line through the arm holding it.
The above reflection (across the angle bisector) accomplishes both rotation and reflection in one transformation.
