can someone help me with this AP Calculus problem?

Question

In exercise 77 and 78 write an equation whose graph has the indicated property.
77. The graph has intercepts at x = -2, x =4, and x = 6
This is the answer for number 77:
y = (x + 2)(x - 4)(x - 6)
I don't understand why though. Why does the signs change from negative 2 and positive 4 to negative four?
I need help solving the one listed below also please

78. The graph has intercepts at x = -5/2, x = 2, x = 3/2

Answer 1

77. The x-intercepts occur when y = 0. Therefore, we have
(x + 2)(x - 4)(x - 6) = 0. But a product of factors = 0 if and only if one of the factors = 0. This implies either x + 2 = 0, or
x - 4 = 0, or x - 6 = 0. Solve these three equations and find that x = -2, 4, or 6.

78. Following the method of 77, we find the intercepts occur at 0 = (x + 5/2)(x - 2)(x - 3/2). Therefore, the equation is
y = (x + 5/2)(x - 2)(x - 3/2) or y = x^3 - x^2 -(23/4)x + (15/2).