I am making an attempt to outline the area between two curves, f[x] and g[x], I can simply discover the place they intersect:

f = Perform[x, 12 x^2];

g = Perform[x, 3 x^3];

p = {x, g[x]} /. DeleteDuplicates[Solve[g[x] == f[x], x, Reals]];

p1 = First[Take[p, 1]];

p2 = First[Drop[p, 1]];

From there i plot the curves:

plot = Plot[Evaluate@Through[{f, g}@x], {x, 0, 4},
PlotRange -> {{0, 4}, {0, 200}},
Epilog -> {Pink, PointSize[0.02], Level@{p1, p2}},
PlotLabels -> Computerized]

And all of that works superb, my drawback is when i try to outline the intersection of these two areas

rf = ImplicitRegion[y <= f[x], {x, y}];

rg = ImplicitRegion[y >= g[x], {x, y}];

intersection = RegionIntersection @@ {rf, rg};

Area[rf, PlotRange -> {{0, 4}, {0, 200}}]