The Xbox 360 version of Need for Speed Most Wanted (2005) does not support split-screen multiplayer. Only single-player and online (Xbox Live) modes exist.
The 360 port was a rushed launch-title upscale of the PS2/Xbox original. Split-screen was cut to meet launch deadline and maintain framerate on the new hardware.
For local racing on 360, Carbon is the superior Most Wanted-era choice.