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Force due to gravitational attraction on the surface of planet 
          = G M m / R² = m g

Hence  g = G M / R²

     G = universal gravitational constant = 6.67 N-m²/kg²
     M = mass of the planet
     m = mass of the body on the surface of planet
     R = radius of the planet

When g is calculated with the values of mass of moon and radius of moon, g happens to be less than the value for Earth.
  Mass of Earth / (Radius of Earth)²   >   Mass of Moon / (radius of Moon)²

So the gravity is more on Earth and numerically is 6 times that on Moon.