Ahh, now I fear that the process is lost from the result. While it might not be realistic expectations to have a perfect replica of the edit from scratch, going down this route might not result in the most amount of this great learning opportunity. So, I will resign my laziness and properly explain my thought process myself

ONE

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Consider the purpose!
Who is the intended audience, and who will be viewing the piece? I scraped together some context and figured this would be quite small, so this helped to determine the direction to take this edit, namely into the style of some cel-shaded, two colored, juicy clustery goodness. Keeping it nice and simple with style and color drastically improves readability at this size.
TWO

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Look at the original!
This is more of an edit specific thing, but I ain't leaving anything out this time! I am not lazy anymore ahhhhh

! Determine what is keep and remove, and whether or not it is easier to draw over the entire thing, especially at small sizes. The basic features and silhouette of this was good, so I stuck with it and just ran over the lighting.
THREE

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The editing.
This is the part where intuition runs over a bit and it gets hard to explain, and it is where I got caught up in explaining enough to enlist the help of the explanation master. First thing to note: pillow shading! There is quite a bit of it, and it shows some lack of fundamental understanding of art basics. It might be a bit ironic since my edit was not exactly the most accurate, but that was a purposeful choice for readability (or a lame excuse, assume at your own discretion

). Breaking the dog head into a semi-dog like head shape is a good first step, and then visualize the head in your head to figure out where the shadow goes. I would give a better demonstration but I am not at my desktop right now :| .
THREEpointFIVE
I needed a break.
Ok now we get into the technique and stuff. This is the most subjective part so I will just use a stream of consciousness for this part and vomit words onto the screen, otherwise I will feel too much like a narcissistic, self-centered anus to continue. First is colors, which were pretty much OK for this. Second is contrast, which was where some of the problems came from with the harshness of the wrinkles on the head. I personally prefer a less intense definition of lines so I eased up on that. I did break up the symmetry as kasumi mentioned, though that was more of a product of sketching out the edit that I didn't really think too much about. I made two main clusters, the lighter color at the top and the lower shadow at the bottom. This is enough to define some volume without being too noisy and overwhelming. The same two color volume definition scheme is used for the nose part and the ears. I also redrew the wrinkles. Here is where the stream of consciousness part gets weird since I am going back to the wrinkles for a bit but w/e. I would like to say use a reference for this but I didn't so I can't really do that, but you should use a reference. Generally for my inside likes for something like a small dent in a region, I go with a lighter colored, thin, tapering line for the dent, in this case, the wrinkles. Anyway, back to the volumes and stuff. After defining how you want to render the shapes, imagine the head as a combination of many shapes and render the shapes individually, and then add cast shadow if needed. Make sure you have a proper knowledge of shading basic shapes in art (cylinders, spheres, etc). Them moving on to stuff like the eyes, which I took a few more liberties on to soften up. Everyone has their own way of doing eyes so it is whatever mostly. I think that is a decent enough explanation. I am really more of a visual guy so without my mouse and ability to draw out what I mean, this is the best you are going to get from me.
So I would recommend just ignoring the edit and try to create something using a process similar to that mentioned above. Or you can not, it is a free world. Good luck!