Ok, so the main difference between your picture and the owl is complexity. So the main problem is not selecting and separating values but the amount you would need to put to mark every place you need to number.
I'm assuming you want to create "paint-by-numbers" for kids so limited pallet, big shapes etc.
You will use a lot of
So the color picker will be your friend
First you would need to select and separate the black outlines. Just use color picker to find the black color go to Select>color range and the pop-up window should show you what will be selected.
Don't be afraid to move fuzziness to 200 and select extra color as you can delete it later. Click OK and then duplicate the layer
Then you repeat this step for every color.
Now a cool trick for those who say
what if I miss some color?
image>duplicate then choose
Image > Mode > Indexed in the index color box set the desired number of colors (don't worry, if your picture don't have 256 color then they won't show). Go to
Image > Mode > Color Table hit save and you have a brand new color swatch for your picture. Just load it and you can easily choose colors to select.
Now, back to our picture. I assume that by now you have every color on separate layer.
On top of layers create new layer and call it "inside outlines". Then select every layer content (but one by one) with
ctrl/cmd clicking on the layer miniature. With
edit>stroke create on the "inside outlines" an outline. Repeat for every color.
Now, on top of that move the first layer with the original outline. Look to see if nothing is confusing or unnecessary (like the lines on his knees). If yes then just erase them. IF your outer outline have this extra spaces with color just select corresponding layer with
ctrl/cmdend use it to delete the unneeded things.
And now what is left is to number the colors. And this is manual labor.