Cutting part of this model

Hey everyone! How could I cut out this part of the model without using boolean modifier?



I know I could extrude the faces and then delete parts of the mesh but I want to do it more simpler.
Oh, and I don’t want to draw lines so I can use knife project.

Delete the faces (X key). First remove your double vertices (select all vertices and W / Remove Doubles)

If you did this on both sides you can then join them by selecting the edges and W / Bridge Edge Loops

Thanks for the help.