Let’s say, I have a logo of website, with size 120x50px.
Favicon should be 16x16px to be supported by major browsers.
How it is possible to rework some image, making it smaller nearly in 10 times, and save the basic look?
As mentioned, you need to re-draw the icon in the correct size.
I’ve found this a bit difficult to do in Photoshop, so what I did was export an image in full size, and then use the favicon.cc generator to adjust the pixels manually. You can do this in any program, but I find this tool quite useful.