The moon's surface gravity is one-sixth that of the earth. calculate the weight on the moon of an object that has a mass of 24 kg.

When we say "The moon's surface gravity is one-sixth that of the earth.",
we mean that the acceleration of gravity on the Moon's surface is 1/6 of
the acceleration of gravity on the Earth's surface.

The acceleration of gravity is (9.8 m/s²) on the Earth's surface, so
it would be (9.8/6 m/s²) on the Moon's surface.

The weight of any object, right now, is

(object's mass) · (acceleration of gravity where the object is located now) .

If the object's mass is 24 kg and the object is on the Moon right now,
then its weight is 

(24 kg) · (9.8/6 m/s²)

= (24 · 9.8 / 6) kg-m/s²

= 39.2 Newtons