On this page of our guide to Layers of Fear 2 we have provided a detailed description of the projector riddle from act 1. You will learn how to use the projector in order to spawn the door that may get you out of the room.
You will get to the projector room soon after you solve the riddle with the safe.
Go to the projector and interact with it. Start scrolling the movie until you stop at the frame with the doors - this shows the attached image.
Step away from the projector and go to the door, so they shall materialize. This will allow you to open them and go further. This way you will solve the riddle.