It took Superman, Wonderwoman, and J'onn to move the earth, not the moon, it was during the Obsidian Age Arc, when they when back in time, searching fo aquaman.
It was Superman, Green Lantern, and Wonderwoman who moved the moon out of it's orbit into earth's orbit. They also pulled it up back out of Earth's orbit(actually making a u-turn with it, the moon) as it was falling into earth's orbit the whole time, making it alot more heavier than what it is when away from the earth, within it normal orbital position. This was in he Terror Incognita Arc, when they once again fought the white martians.
Superman has moved the moon on his own, he wouldn't need any help moving it some, but the moon falling into the earth and needing to be moved out of earth's orbit at precisely the moment mentioned to prevent earth from being severely damage by the moon falling into its orbit is something that would take great effort and some or a few very powerful, elite physically strong characters. That's is why they were struggling in that Arc, it was a one-time only, very high stakes, rare and awesome feat that only a few, working together could achieve without destroying the planet and life on earth.