i've managed to make need for speed carbon run and play on windows 10 64-bit
here's how: i installed the game using the game disk
: downloaded a normal game "crack"(NFSC) which helps run and play the game without the game disk(dvd)
: copied the "crack" and pasted it within the installed game found under: C:\Programs or Program files(x86)\Electronic Arts\
: And After Doing That.....The Game Will Definitely Work On Windows 10 And Lastly Check "Compatibility Mode" making sure That it's on "Windows XP Service Pack 3" And Also Make Sure That The Checkbox For "Run this program in compatibility mode for:" Has a Been "Ticked"(Checked)