Oh come on. Surely you know this.
Find where g(x) is NOT differentiable.
I know that functions arnt differentiable at corner points or points of vertical tangency...but how do i go on about finding the actual values where they are not differentiable??
Suppose f is differenciable at x_0 and g is differenciable at f(x_0) then g(f(x)) is differenciable at x_0. Now |x| is differenciable where x!=0 so if 2x^3 - 3x^2 is non-zero then |2x^3 - 3x^2| is differenciable at that point. Then you need to check the zero points to see if they are differenable.
Plato gave a good tip - it works well for this question You get x = 3/2 as the only point where the function is not differentiable.
In general, you can always draw a graph of f(x) then reflect in the x-axis the parts lying below the x-axis to get |f(x)|.
The 'corners' (I personally prefer calling them the 'pointy bits'. Their technical name is salient points) are then obvious and will be x-intercepts. But note that not all x-intercepts will be 'corners' ..... (for example, in your present question x = 0 is NOT a corner).