To solve this system of inequalities, we need to find the values of x that satisfy both inequalities.

First, we'll solve the inequality 2x + 4 > 5x - 8:

2x + 4 > 5x - 8
4 + 8 > 5x - 2x
12 > 3x
4 > x

Now, we'll solve the inequality 3x + 2 < x + 4:

3x + 2 < x + 4
2 < x + 4 - 3x
2 < 4 - 2x
-2x < 2
x > -1

So, the solution to the system of inequalities is x > -1 and x < 4. Therefore, the solution set for the system of inequalities is -1 < x < 4.