If $h/4\pi\to 0$ in the Heisenberg's uncertainty principle what happen? If in the Heisenberg's uncertainty principle the quantity 
$$\frac{\hbar}2=\frac{h}{4\pi}$$ is near to $0$, what happen?  What is a simple any explanation that could be given to a high school student?
I have read this: Zero Planck constant, but I found lots of different information that still cause confusion in my mind.
 A: Planck's constant has a fixed value, $h = 6.626 \,070\, 15 \times 10^{−34}\:\rm J \: s$, which does not depend on any aspects of the state or structure of any given system. This implies that the limit "$h\to 0$" is a completely meaningless gesture. Planck's constant cannot be changed, either up or down, so "making it go to zero" is not something that can be done.
In particular, this means that speculating what will happen to X bit of physics (be it the Heisenberg uncertainty principle or anything else) when "$h\to 0$" is pointless, as the premise is unphysical.
The same goes with "$h\simeq 0$" $-$Planck's constant has a value and it is nonzero. Saying that "$h\simeq 0$" is meaningless.

Nevertheless, what you're describing does have a very closely related concept which does make sense, known as the correspondence principle. 
The core intuition that expressions like "$h\simeq 0$" are trying to capture is the basic question

what happens when the dynamics of a system happens on scales at which $h$ is so small as to be irrelevant?

but that question is phrased the wrong way round: it's not that $h$ is small, it's that the characteristic scales of the dynamics of the system are large compared to $h$. So what happens then? basically, you recover the classical limit of your quantum system, i.e. the system behaves more and more like a classical system, and quantum behaviour becomes less and less pronounced, until it is no longer visible.
If you want further details, ask a question in a way which is suitably detailed in a way that correspond to the level of detail that you're expecting in the answer. And, of course, before asking or editing, be sure to research appropriately the several hundred questions on the classical limit and correspondence principle already on this site.
