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The formula for the area of a triangle is A = 1/2 * base * height.
Given that the area is 24 square inches and the base length is 6 inches, we can plug in these values into the equation to solve for the height.
24 = 1/2 * 6 * height
24 = 3 * height
height = 8 inches
Therefore, the height of the triangle is 8 inches.
Answer: 8 inches