g(x)<0 in this case is:

(x-2)/(x+4)<0;

The ratio of two numbers is less than zero when one is positive and another one is negative.

So we have two cases:

x-2<0 and

x+4>0

OR

x-2>0 and

x+4<0

In the first case,

x<2 and

x>-4,

which is equivalent to -4<x<2 or x∈(-4;2)

In the second case,

x>2 and

x<-4

There is no way that x can be simultaneously greater than two and less than -4, so there is no solution for the second system of equations. Or it is said that the solution is the empty set of points. Anyway, the solution to the inequality is the union of two sets: the solution to the first case and the solution to the second case. Since the second case has no solution, the union is just the set of x for the first case.

Thus the answer is

**-4<x<2 or x∈(-4;2)**