Mass has units of kilograms and does not change with gravity. A 10 kg object will still have a mass of 10 kg on the moon.
Weight is the force on an object due to gravity. It is given by the mass multiplied by the acceleration due to gravity. It is a force and is measured in units of Newtons.
So weight depends on the acceleration due to gravity, which depends on the gravity of the planet or moon you are on.
On Earth, the standard value for the acceleration due to gravity at the surface is
On the moon,
Therefore, an object with a mass of 10 kg has different weights on Earth and the Moon:
But its mass is the same in both places.
In the question, you stated that the object weighs 10 kg. From a physics point of view, this is incorrect. The object weighs 98.1 N and has a mass of 10 kg. But in everyday life we usually confuse the two and use weight to talk about the mass of an object.