As of 2021, officially retired Need for Speed: Carbon along with several other older titles. This means:
You can no longer purchase digital versions from the EA App , Steam, or other major storefronts according to reports on Wikipedia . need-for-speed-carbon-game-free-download
The only 100% legal way to own the game now is by purchasing a used physical disc from secondary markets like eBay or Amazon. Beware of "Free Download" Sites As of 2021, officially retired Need for Speed: