Finding the area of a region? I sketched out the graph to get this figure but I can't seem to find the area of the shaded region... would one Y = 4 and the other Y = 8? 
I, in all honesty, am so flabbergasted with this question, any guidance will be much appreciated. I got 28/3 for the first integral (0 to 4) and 292/3 for the second integral (4 to 16)... I feel like I'm doing this wrong.
Okay, I'm going to be honest, can someone please solve this for me? I got 320/3 as my final answer and yet it's still wrong, I'm just about given up at this point, it's literally my last question of this semester.

You need to set up two double integrals.
The first one:
$\int_0^4 \int_{.5x}^ \sqrt{x} dydx$
The second one:
$\int_4^{16} \int_\sqrt{x}^{.5x} dydx$
The computation is straightforward.
