The x-intercepts of y = f(x) are the points where y is equal to 0.

-6x^4-23x^3-23x^2+2x+8 = 0

=> -6x^4-12x^3 - 11x^3 - 22x^2 - x^2 - 2x + 4x + 8 = 0

=> -6x^3(x + 2) - 11x^2(x + 2) - x(x + 2) + 4(x + 2) = 0

=> (x + 2)(-6x^3 - 11x^2 - x + 4) = 0

=> (x + 2)(-6x^3 - 6x^2 - 5x^2 - 5x + 4x + 4) = 0

=> (x + 2)(-6x^2(x + 1) - 5x(x + 1) + 4(x + 1)) = 0

=> (x + 2)(x + 1)(-6x^2 - 5x + 4) = 0

=> (x + 2)(x + 1)(-6x^2 + 3x - 8x + 4) = 0

=> (x + 2)(x + 1)(-3x( 2x - 1) - 4(2x - 1)) = 0

=> (x + 2)(x + 1)(-3x - 4)(2x - 1) = 0

=> x = -2, x = -1, x = -4/3, x = 1/2

**The x-intercepts of the graph of y = -6x^4 - 23x^3 - 23x^2 + 2x + 8 are (-2, 0), (-1, 0), (-4/3, 0) and (1/2, 0)**