Welcome, suspect0!
Yes, you can attack zombies in your own territory.
From page 15 of the Rulebook (Combat Movement):
Units can move freely through friendly spaces en route to hostile spaces during this phase. Units cannot end their movement in friendly spaces during the Combat Move phase except for the following instances:
Tanks that have blitzed through an unoccupied hostile space (see “Tanks and Blitzing”).
Sea units that will be participating in an amphibious assault from an uncontested sea zone (see “Amphibious Assaults”).
Units moving from a hostile sea zone (see “Sea Units Starting in Hostile Sea Zones”) or from a friendly space where combat will be initiated to escape combat as their combat move.
Units moving into a sea zone containing only enemy submarines and/or transports in order to attack those units. (Remember that such a sea zone is not considered hostile.)
Units that are attacking zombies in a friendly territory.
And from page 19 (General Combat):
In this step, you resolve combat in each space that contains your units and either contains enemy units or is enemy controlled. You may also resolve combat in each friendly territory that contains your units and zombies (in fact, you must do so in such territories that you moved units into during the previous phase).
Note that when you’re attacking only zombies, both “normal” hits and “zombie” hits (6s) by your units are applied to zombie units. It’s easier to kill zombies when you don’t have to worry about the enemy.
I’m glad you’re enjoying the game. Have fun!
