The graph on the left is $K_6\text{.}$ The only way to properly color the graph is to give every vertex a different color (since every vertex is adjacent to every other vertex). Thus the chromatic number is 6.

The middle graph can be properly colored with just 3 colors (Red, Blue, and Green). For example:

$Six vertices arranged in a triangle (with three vertices along each side). Six edges form the outside of the triangle, and three edges connect the center vertices of each side (in an upside-down triangle). The bottom row of vertices are labeled R, B, G (left to right), the middle row of vertices are labeled G, R, and to top vertex is labeled B.$

There is no way to color it with just two colors, since there are three vertices mutually adjacent (i.e., a triangle). Thus the chromatic number is 3.

The graph on the right is just $K_{2,3}\text{.}$ As with all bipartite graphs, this graph has chromatic number 2: color the vertices on the top row red and the vertices on the bottom row blue.