Answer:
The object obeys the equation
F = M a on both the earth and the moon (mass does not depend on location)
The problem is a little misleading because if an object has a mass of
10 kg then its weight is 10 kg * 9.8 m/s^2 = 98 Newtons
That means that weight is not expressed in Kg but rather in Newtons
Newton's Law is true on the moon as it is on the earth and F = M a
An object that weighed 10 N on earth would weigh 10 / 6 = 1.67 N on the moon
One must take care in describing a force in units of Newtons not in Kg