There are several ways something like this could be accomplished. To do it, you will have to understand most of what is here:
AI2 free online eBook http://appinventor.mit.edu/explore/ai2/tutorials.html ... the links are at the bottom of the Web page.
You have to learn to use the Logic blocks, the If ..then control etc.
I see two ways of doing this, one using a Canvas control where all the images are sprites the second way to do it is to use Buttons with the images in the buttons...you can add an image to a button. Neither method is easy for a beginner.
I suggest you pick one basic method, then start trying things.
For Using a Canvas.... the Touched block will be very important. You have the ability to hide sprites by making them visible or invisible using true or false logic blocks, you will need If..then blocks etc.
For using Buttons, you will have to preposition some buttons and hide the ones you are not using...with AI2, you can not drag and drop a button anywhere on the screen (however with a Canvas, you can do exactly that).
I hope this gives you a start. This is your project and you are going to have to figure it out unless some provides you with some specific code. Can manipulating the images as you demonstrated be done? Yes, and it is not very difficult, it just will require writing complicated block code and a few hours of coding, perhaps less if you understand all the AI2 coding principles.
Try some blocks. I suggest you make a small project to experiment with...either using the Canvas or images.
I hope someone else will also give you some hints.
Regards,
Steve