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To find the height of the rectangle, you need to find the area of the triangle and subtract it from the total area of 78 square centimeters.
The rectangle's total area is 6x13 = 78 square centimeters.
The triangle has a base of 6 cm (since the rectangle is 6 cm wide) and a height of (13-8) = 5 cm.
Area of the triangle = 1/2 x base x height = 1/2 x 6 x 5 = 15 square cm.
Subtracting the area of the triangle from the total area:
78 - 15 = 63 square cm.
Since the rectangle's height is 8 cm, the answer is:
8 centimeters.