Explain the difference between mass and weight. Why is your weight on the Moon one-sixth that on Earth?

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The weight on moon is $(1/6)^t^h$ of the weight at earth because the value of g reduces to $(1/6)^t^h$ on moon.

Mass is a measure of the amount of matter in an object, and Weight is the amount of force that gravity exerts on an object.

What is the relation between mass and weight?

The main difference between mass and weight is: Mass is a scientific measure of the amount of matter an object is made of. Regardless of where you are at any given moment, the mass is constant.

However, weight is actually a description of gravity on an object.
The relation between mass (m) and weight (W) is $W = m * g$ . Thus, weight is defined as the product of mass and gravitational acceleration (g)
As weight depends on the value of gravitational acceleration, it changes as the value of g changes.
Now, the value of g at moon is $(1/6)^t^h$ of the value of g at earth, that means the weight on moon is $(1/6)^t^h$ of the weight on earth.