First let’s clean up some minor errors. First, the volume is $8000$ units cubed; if it were squared, it would be an area. Next, it’s incorrect to write $s^2h=8000=h=8000/s^2\;:$ you don’t really mean that $h=8000$. Your second $=$ doesn’t mean equals; it means something like implies. You should write $s^2h=8000,\text{ so }h=\frac{8000}{s^2}$ or something of the sort.
Now let’s get to the meat of it. I’ll use $A$ for the surface area of the box, which I assume is a square box with no top. If so, you’re quite right: $A=4sh+s^2$, and when you combine this with the volume requirement, you get $A=4s\left(\frac{8000}{s^2}\right)+s^2\;,$ which you could simplify to $A=\frac{32000}s+s^2\;.$
Now why did you set this equal to $0$? That would make the area $0$, which is plainly impossible.
You want to minimize $A$: to find the values of $s$ and $h$ that make $A$ as small as possible. Since you already know how to get $h$ from $s$, you really just have to find the value of $s$ that minimizes $A$. That’s a basic calculus problem: find the minimum of the function $A(s)=\frac{32000}s+s^2\;.$ To do that you first find the derivative A'(s), then set that equal to $0$ to find critical points, and proceed from there. I’ll let you take a crack at that on your own before I go any further.