Question

The Moon takes 27 days to complete a revolution around the earth but it takes 29 days to come back to a full moon. Why??

Answer 1

It takes the moon 29 days, 12 hours, 44 minutes, and 2.9 seconds to complete a rotation. It takes the moon 27 days, 7 hours, 43 minutes, and 11.5 seconds to go around the earth. The rotation during the revolution causes the moon to always have one face only visible to the earth, with slight variations (librations) showing a little bit extra here and there.
The earth rotates counter clockwise as viewed from a north of the earth position. The moon revolves around the earth in a counter clockwise motion again as viewed from a position north of the earth.