The minimum number of colors is 4.
Work Step by Step
For convenience, instead of coloring, the countries in the provided picture are filled with numbers, instead of colors, each number representing a different color. From the picture, we can see that it's possible to paint them so that no country has the same color as any of it's bordering countries with 4 colors. It's impossible to paint them all with 3 or less colors without 2 neighboring countries having the same color.