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First, find the x-intercepts by setting y = 0:x³ - 6x² + 8x = 0x(x² - 6x + 8) = 0x(x - 2)(x - 4) = 0The x-intercepts are x = 0, x = 2, x = 4.The area is calculated by integrating the absolute value of the function over the intervals defined by the intercepts.The function y = x(x-2)(x-4) is positive between 0 and 2, and negative between 2 and 4.Area = ∫₀² (x³ - 6x² + 8x) dx + |∫₂⁴ (x³ - 6x² + 8x) dx|Find the indefinite integral: ∫ (x³ - 6x² + 8x) dx = x⁴/4 - 2x³ + 4x². Let F(x) = x⁴/4 - 2x³ + 4x².For the first interval [0, 2]:F(2) - F(0) = (2⁴/4 - 2(2)³ + 4(2)²) - (0) = (16/4 - 16 + 16) = 4.For the second interval [2, 4]:F(4) - F(2) = (4⁴/4 - 2(4)³ + 4(4)²) - (4) = (64 - 128 + 64) - 4 = 0 - 4 = -4.Total Area = 4 + |-4| = 4 + 4 = 8.