Any expert here know how 2 solve this problem using Maple?

I don't know maple from a tree.
but if f(x)=x^(1/3) & g(x)=2x^2-4
you can set the intersection as the point where f(x)=g(x) or
x^(1/3)=2x^2-4
then
x=[2x^2-4}^3=8[x^2-2]^3=8[x^6-6x^4+12x^2-9]
this results in the polynomial
8x^6-48x^4+96x^2-x-64=0
However because the degree of this polynomial is >4 an exact solution does not exist

So if I was to find a solution (there are t real selations) would be to plot f(x) and g(x) and find a graphical intersection and use these as a starting point to walk toward a zero on the combined polynomial. You'll get to your required 10 decimal points by iteration.

Rap