If matter cannot be created nor destroyed, how does mass ( defined as the amount of material, or matter within an object ) increase as an object approaches the speed of light?

Do some googling. It's all over the place.

Here's one:

Answer 3 - Mass and Speed - Perimeter Institute for Theoretical Physics (http://www.perimeterinstitute.ca/Outreach/Education/Answer_3_-_Mass_and_Speed/)