According to Microsoft,
Halo 4's multiplayer mode will require 8 GB of free space.
This is controversial for Xbox 360 Arcade and Core consoles, seeing as how their starting 4 GB won't even be enough to cover the most anticipated experience Halo 4 is offering.
External storage like USB hard drives will work, but Microsoft recommends a larger internal hard drive for the 360 for an "optimal experience."