I can't find the right definition for the thing that you see on the right. If we put all parts of it together we will get a box that we can rotate (this picture is taken from a quiz for kids - they need to guess which picture they will see if they look at each cube from the top).
But what is this unfolded thing on the right called in English correctly, in a single term? I found the word "scan" but I'm not sure it is a correct one. 
The word is net.
I'm a maths teacher, and this is the standard term used in Australia. I'm fairly sure it's the same in other parts of the English-speaking world, thanks to sources like:
It's worth noting that this is not a common thing for most people to talk about, and unfortunately, "net" also has other (more common) meanings. A descriptive phrase, like your "unfolded thing", would be useful to name it when talking to people unfamiliar with the correct name.
User @Tim Pederick suggests the word “net”, which mathematicians will recognize. For the general public, it's difficult to find a single word to describe the "unfolded cube" in the picture.
A "scan" is not quite correct, because we use that word to mean when a scanner takes a flat picture, or a 3D representation of something.
In the context of mechanical engineering, when someone creates an engineering drawing ("blueprint"), a layout of multiple views together might be called a multiview drawing (MIT Open Courseware), like this:
The difference here is that you have modified the object (by unfolding it), so multiview drawing is close, but not quite right.
The word diagram (as opposed to picture) carries the meaning that something has been changed. A diagram can be a simplified version of something.
A similar word is a "schematic" (noun) or a "schematic representation" or a "schematic drawing" or a "schematic diagram". This emphasizes that the drawing is not meant to be exactly like reality, but that it is supposed to help explain how something works.
Electrical engineers use schematic drawings to help understand circuits, but their drawings are not usually arranged in the exact same way that the physical components are laid out.
Your question used the word “unfolded” which is pretty descriptive. How about simply an “unfolded view“.
This is straightforward(Definition) and clear — the best kind of writing!
In mechanical engineering, 3D CAD and arts & craft such drawings are called unfolded though sometimes people also refer to them as unwrapped.
Software designed to generate such diagrams from 3D models are marketed as unfolding software and the term has been intuitively understood across multiple industries/communities.
I would call that an unfolded box too. And perhaps if you omitted a panel it would be an unfolded open-topped box.
For a non-technical audience, you might use 'breakdown' as in "the breakdown of the cube shows..."
This figure is difficult to describe using only one word. Some further explanation and elaboration will probably be required.
projection: MW 1.b
the process or technique of reproducing a spatial object upon a plane or curved surface or a line by projecting its points.
also : a graph or figure so formed
Calling a drawing a "flat projection" emphasizes that perspective is not taken into account:
flat projection A method of drawing what is directly visible from a point perpendicular to the line of vision, with no adjustments for perspective.
Technically you could call the drawing on the right the cube's "flat projection".
For general readership you could simply call it "the cube in projection", as in "here's six pictures of each side of the cube projected onto the flat surface you're looking at".
