When you enter the marked door, you will emerge into a stairwell. Start leading your squad up the stairs, only to find a licker on the ceiling shortly after the stairwell begins. Shoot it down from the ceiling before it can catch you in its lengthy grasp. When it hits the ground, repeatedly stomp on it until it dies in a frothy burst. Keep climbing the stairs until you reach the top. Head through the door to the far side of the balcony. Be careful of the trip mines lining this area. Shoot them all before proceeding forward.
Once you reach the top of the area, you will find a large group of enemies inside of the open doorway. Shoot the explosive zombies first, as there is a chance that they will take out some of their own in the resulting explosion. Look to the left to find another group of zombies feasting on one of their fallen comrades. Toss a grenade right in the middle of them, on the corpse that they are eating, to blow them all sky high. However, when you take them out, be prepared to turn and fight more explosive zombies, who will emerge from behind the desk. As usual, aim for the red explosive bits.
Search around the area to find three pieces of Intel on the various desks and shelves in the room. When you have collected them, upload them to the Laptop in the back of the room to gain a good chunk of experience. Look to the desk where the explosive zombies emerged from to find another Security Camera on the wall just to the left. Take it out, and then get to work on disarming the trip mines blocking access to the marked door. Once it is clear, head through the door to reach the balcony overlooking the cafeteria from which you entered the building. Head to the right before proceeding to the objective to reach a new staircase that contains supplies. Restock on ammo here, then return to the door in the stairwell and open it up. Head down the stiars to reach more supplies. You will find a piece of Intel here, along with Antiviral Spray, First Aid Spray, and an ammo locker. Heal up and climb back up the stairs to where the trip mines are. Shoot the mines and proceed through the door.