First of all, go pick up a game engine. You can learn by following examples, and experimenting. And of course, reading the documentation when you don’t know something… And if you get stuck, come back and ask here.
As per your question…
flipping a games X axis rendering so everything that was on the right is now on the left, and vice versa.
For most engines, you apply a transform to the root of level/stage/scene/prefab/whatever (depending on the engine) that contains the geometry of the world. You keep that transform separate from the player avatar, the UI, and anything else that remains unchanged. Then the mirror mode, is a matter of modifying that transform to one that flips the X axis.
Some additional tweaks might be necessary, such as changing the starting position of the avatar (assuming it does not always start at the coordinates 0). Do not forget to test your game.
In case that is not possible… Ask an engine specific question, there might a way around it.
You might be able to do something similar with a vertex shader, if you only need it as a visual effect.
See the documentation of whatever engine you picked to see if they allow you to write custom shaders. For any popular enough engine, you should be able to find tutorials online, with a simple search.
For 3D, you would declare a vector uniform and multiply the vertex coordinates by it in the vertex shader. Set it by default to 1 in all axis. So that when you multiply, it changes nothing, as any value times 1 is the same value. And to flip the X axis, you set it to -1 on the X axis and leave it at 1 in the others.
For 2D, you would instead want to flip UV coordinates. The plan is to make the textures appear reversed. It is the same idea. You declare a vector uniform and multiply the UV by that vector.
Note that using a shader to do this is just a visual change. If the game engine is handling physics, it would not take this effect into account for that. However, if you flipped everything (with the transform), and you need to revert some items (e.g. pickups should look the regular way), this can be a quick fix (as opposed of going over every transform of every item you want to unflip).
We can argue about another way to flip everything: post-processing. The idea is that you will take the image from the game, then flip it, and then you show the flipped image.
Depending of the engine, the particulars change… Hopefully you can attach a fragment shader for post-processing (either globally or to the camera).
Alternatively, your engine may allow you to set a camera to render to a texture, and then you can have a second camera that looks directly to a quad that covers its view perfectly. And have that texture on the quad, except it is flipped (flipped texture means flipped UV coordinates).
Or, if your engine is so inclined, you might be able to simply have that quad in-front of the camera at all times, and tell the engine to render that quad after everything else.
Please, see a tutorial on post-processing for the engine you choose.
You could tell the engine to render UI elements afterwards (for engines that allow that). Or you could render UI elements reversed to begin with.
You may have to modify the input controls to revert the axis. So that going to the right, still appears to go to the right. Despite it actually going to the left, except the left appears to the right because the image is flipped. And similarly for going to the left. Hopefully that makes sense.
Baring using shaders to those changes, it could be possible to write an script to go over everything either flip the transforms or the UV coordinates.
If your engines does not let you write custom shaders, nor attach such scripts, then that is not a great engine. However, you could take the 3D models into an editor (e.g. Blender) flip them there, and export them again. For 2D you could take the textures into an editor (e.g. Gimp) flip them there, and export them again. It would result in a lot of extra size on the final game, since it would have both the regular versions and the mirror versions of everything. Or you can pick a better engine.