You will likely get more submissions that are closer to what you want than my rendition.
Note that the image you gave as an example was not created algoritmically from a photograph (maybe only as a reference).
In converting an image, removing a lot of detail is needed to start to get the cartoon effect.
What I did was use Adobe Illustrator with its automatic trace function as a small number or grayscale levels, exported as PNG, then overlayed the original in Photoshop with a blend mode of color.
This is only to give you one direction.
There are many add-ons or other tools that can convert images to cartoon like that could be considered.
I took a try at it using several filters including cutout, posterization, and oil filters. Combined all the layers into a single layer then placed the original image underneath.
Using blend if, brought the original image back in to increase detail. Then replaced the sky overall to a single color.
I agree with @thebestcpu that the sample shown was done in a program like Illustrator from scratch.
Did my best...