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counting and probability intermediate

Problem

Link is coloring a triforce, which consists of four equilateral triangles and is depicted below. He has three colors to use: gold, black, and green. So that it remains recognizable, he doesn't want to color any two triangles the same color if they share a side. How many different ways can he color the triforce? (Two colorings that differ by rotation are considered distinct.)
problem
Solution
There are 3 ways to choose a color for the center. Once the center color is chosen, for each of the remaining triangles there are 2 ways to choose a color (any color except the center color). Therefore, there are ways to color the triforce.
Final answer
24