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The original photo has an area of 6 cm * 4 cm = 24 square centimeters.
When resized into a postcard with a length of 15 cm, the width will be 15 cm * (4/6) = 10 cm.
Therefore, the area of the postcard will be 15 cm * 10 cm = 150 square centimeters.
Therefore, the correct answer is: 150 square centimeters