Teams were supposed to infer from the picture of the flag on the moon, from the eight different phases of the moon pictured, from the clear pairs of moons, and the circular orientation of those phases, that this clue was encoded in semaphore.
The next step was to figure out where to put the phases around the earth. Teams noticed that the sun was obviously shining from the right. Some teams correctly noticed that the the moon should not look full looking into the plane of the earth-sun system. Rather than a representational picture of the moon, the full moon on the right was meant to indicate what the moon would look like from the earth when in that position relative to the earth and the sun. So, when the earth is between the sun and the moon (absent the rare lunar eclipse) the entire bright side of the moon is visible to earth—hence a full moon. Moreover, because the image of the earth shows the north pole (look closely), teams should know that they are thinking about the moon's appearance from the northern hemisphere. This is represented by the following diagram from this site.
Decoding each pair of moons yields:
or the Lawrence Hall of Science at the University of California, Berkeley.