The important thing to understand about mechanized infantry movement is that they move in exactly the same way that tanks do, except that they can’t blitz without a tank. In most cases, the confusion on this issue comes from the definition of the term “blitz”.
Many people define “blitz” as any two-space movement by a tank, but that’s incorrect. A blitz movement is a combat movement through an unoccupied, enemy-controlled territory and into another territory. Only the first territory is “blitzed”. The second one is not, regardless of its status.
So, mechanized infantry may only make a combat movement through an unoccupied, enemy-controlled territory and into another territory when paired with a tank. Any other two-space movement that a tank can legally make can also be made by a mechanized infantry without an accompanying tank. This means that mechanized infantry may always move two friendly spaces alone in noncombat movement, and they may also move two spaces alone in combat movement if the first territory is friendly.
