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The area of the original photo is 6 cm x 4 cm = 24 square cm.
To resize the photo to the length of 15 cm while maintaining the same ratio, we need to calculate the width of the resized photo.
4 cm * (15 cm / 6 cm) = 4 cm * 2.5 = 10 cm
So the new dimensions of the photo will be 15 cm x 10 cm, and the area will be:
15 cm x 10 cm = 150 square cm
Therefore, the area of the postcard will be 150 square centimeters.
Answer: 150 square centimeters