In the diagram below, we want to color two of the dots red, two of the dots green, and two of the dots blue, so that each pair of dots of the same color is joined by an edge. How many ways are there to color the dots?
I looked at scenarios.
If both red are on the outside triangle there are 3 ways to choose which
For each of those ere are 2 ways to place the other colours. Equalling 2*3 = 6 ways
If both reds are on the inside triangle there a 3 ways to chose the dots then 2 ways to place the other colours so that is another 6
If one red is inside and the other outside then there are 3 ways to choose where then there are 4 ways to place the other colours = 3*4=12
So I think that there are 6+6+12 = 24 ways.