Since the game is no longer available for purchase, many fans turn to preservation sites.
If you do manage to download or install the game, you will likely need a few tweaks to make it work on a modern PC: Go to product viewer dialog for this item. Need For Speed: Carbon (pc, 2010) Game & Cardboard Sleeve
Because it is no longer sold by Electronic Arts, it is often classified as by the gaming community. 1. The Legal Route: Physical Copies
The only 100% legal way to own the game now is to purchase a used physical disc.
If you are looking to download for PC today, the situation is a bit tricky because the game has been officially delisted from digital storefronts like the EA App and Steam since 2021.