Head inside the cinema and take out all the undead. Be warned though that there's a lot of infected inside so you may hold them off by the stairs or doorway to avoid getting flanked. Once cleared, go outside the window in the cinema and lower the ladder to make it easier for you to go back just in case. Go downstairs and breach the door in the lower floor and kill the walker inside.
Head to the auditorium and clear the zombies inside. Backtrack your way to the projector room and talk to Jacqueline. She'll then tell you activate the security shutters.
Head back to the breached room earlier and activate the security shutter. Next, grab the key on the table then head to the rear door. Open the control panel with the key then use it to lower the shutter.
After the scene, talk to Marvin to complete the quest.