2025 AMC 10B Problem 16

A circle has been divided into 6 sectors of different sizes. Then 2 of the sectors are painted red, 2 painted green, and 2 painted blue so that no two neighboring sectors are painted the same color. One such coloring is shown below.

How many different colorings are possible?

\textbf{(A)} 12 \qquad \textbf{(B)} 16 \qquad \textbf{(C)} 18 \qquad \textbf{(D)} 24 \qquad \textbf{(E)} 28

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.