There are a couple of alternatives to what you showed that may be faster.
1. The same effect of reducing an image to a specific number of colors is gotten by going to the Image menu, the Mode submenu, and selecting "Indexed color..." At that point you have many palette options, but a fast one is simply selecting "Local (Perceptual)" and inputing the number of colors you want. Once you figure out how to do this and get comfortable with it this can be done in about 10-20 seconds if you don't need to fine tune it.
2. Go to the Filter menu, the Artistic submenu, and select "Cutout..." This option is limited to only 8 colors or less, but gives a few slider bars for adjusting how you want it to look. Again, it should take less than 20 seconds.
I think it would be preferable to post photos and complete information on this site rather than offsite. This statement appears in the description of a few of the forum sections of WetCanvas- "Using offsite links to show your images is not acceptable or in keeping with the intent or spirit of this site and may be removed by the Moderators. Please post images of your work here with the Uploader or Attach them."
Instead, many people here post a link to their blog or whatever else in their signature.