What @A.C.A.C is getting at is (I think) is speed relative to what?
The Earth moves with a speed around the Sun, but that is not an absolute speed, that is a speed relative to the Sun. The Moon has a speed that it orbits the Earth, and another at which it orbits the Sun. I think you are attempting those two together, but those are two different references. You can somewhat do so, and say that you come up with a speed that the moon is orbiting the Sun.
We will ignore that in reality the Earth also orbits the Moon part as it it relatively unimportant here, the Moon is at times effective going around the Sun faster than the Earth, but only while its orbital direction matches the Earth's orbital direction around the Sun. Half the time it does not, half the time it is in the other direction, which means at those times it is orbiting the Sun slower than the Earth. If you are talking average speed relative to the Sun, then the Moon has the same average orbital speed on the Sun as the Earth, however, because it is also orbiting Earth it ends up with a slightly longer orbital path, so a slightly higher average orbital speed relative to the Sun.
But the, the entire Solar System is also moving in the Galaxy because it is spinning at a much higher speed than the relative orbital speed of the Earth or Moon. Is that in a direction that adds to of subtracts from the Orbital speed? Oh, Wait, not only is the Galaxy is also moving through space at a much higher rate as well, that really makes it complicated in deciding, relative it what is anything moving faster than anything else. You need to set a point of reference first.
ETA: This link may help to the clarified question: https://en.wikipedia.org/wiki/Talk%3AOrbit_of_the_Moon
This shows a highly exagerated scale what the Earth-Moon orbit around the sun looks like in this image:
Note that the smooth orbit we think of as Earths is not either, it is a two body system orbiting the sun and the moon and Earth actually orbit a center of gravity between them, it is just much closer to the Earth. The picture again is grossly out of scale.