To solve this equation, we first need to find a common denominator for all fractions involved:

3/x - 6/ x(x+2) = 8/ x^2 - 4
3/x - 6/ x(x+2) = 8/ (x+2)(x-2)

Now, rewrite the equation in terms of the common denominator:

(3(x+2) - 6)/x(x+2) = 8/ (x+2)(x-2)

Expand and simplify the left side of the equation:
(3x + 6 - 6) = 8/(x+2)(x-2)
3x = 8/(x+2)(x-2)

Now, multiply both sides by (x+2)(x-2) to get rid of the denominator:
3x(x+2)(x-2) = 8
3x(x^2 - 4) = 8
3x^3 - 12x = 8

Rearrange the equation:
3x^3 - 12x - 8 = 0

[This is a cubic equation, and can be solved using various methods such as graphing, numerical methods, or algebraic methods like synthetic division or factor theorem.]

It can be further simplified or solved using any preferred method.