I am adding a new 12'x24' addition onto the back of my 24'x24' 2-story home(90 years old). The floor joists will run the same direction. Each existing vent is fed by it's own 6" pipe from the furnace. What is the best way to heat and cool this new addition? Can I or should I cut round 6" holes through the 2x10 between the foundation and floor? Any advice would be great.

I can't answer the cutting question specifically, but are you expecting your current furncae and AC to handle the new addition?

Alterations to the duct work usually have to be approved by the people who issue the building permit.

A manual D calculation (Duct work design) and a Manual J (Heat load ) will have to be preformed for the addition.

You could and maybe should consider a separate HVAC unit for the addition.