The figure can be colored in 729 different ways, as each hexagon can be colored either red, yellow, or green, and no two hexagons with a common side may be the same color.
To color the figure in different ways, we must consider that each hexagon can be colored either red, yellow, or green. No two hexagons with a common side may be the same color. This means that for each hexagon, there are three possible choices. Since there are six hexagons in the figure, there are 3^6 = 729 possible ways to color the figure. We can calculate this by multiplying 3 (the number of color choices) by itself 6 times. This gives us the total number of possible color combinations for the figure. As each combination is unique, this means that there are 729 different ways to color the figure.
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