Question

explain why samples of gold and copper can have the same extensive properties, but not the same intensive properties

Answer 1

Extensive properties, as volume and mass, depend on the amount of material. So, you can have a sample of gold and a sample of copper with the same volume as long as you have different amount of each one.

On the other hand, intensive properties do not depend on the amound of material but on the chemical constitution of the material. Density is an intensive property, so gold and copper have different densities. That is why you can use intensive properties to characterize different materials.