Halo 4 multiplayer will have an 8GB install size
The multiplayer components for Halo 4 will require players to go through an 8 gigabyte installation for optimal performance. Players who do not have a big enough hard drive or USB stick will need to start saving fast.
"At a minimum, you’ll need at least an 8GB USB Flash Drive or an Xbox 360 Hard Drive to play Multiplayer mode in Halo 4. For an optimal experience playing with an Xbox 360 Hard Drive is highly recommended." Reads the Xbox.com product page on Halo 4s multiplayer and optimizing the online experience.
It's also possible that the Spartan Ops campaign, which has been set to contain over 50 missions to play and 12 additional hours of gameplay will increase the space needed for Halo 4 on your Xbox 360s HDD. We're going to go delete some arcade titles now.