How do I cut a hole in the plane using the hollow line loop in the middle they're part of the same mesh and both 2d.
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You could convert your objects to curves and select 2D under the curve options. Doing this gives you a bit more flexibility as you can tweak the loop and see the changes as you do so. Use AltC > Curve from Mesh/Text to do this.
Once you are finished tweaking, convert back to a mesh with AltC > Mesh from Curve/Meta/... You will notice that the plane is triangulated. To clean this up, run a Limited Dissolve on the mesh.
This can be done using Knife Project, however for the case you show to work, you will have to use a recent Blender build, since improved knife support was added after 2.69 release.
To use Knife Project, in Object mode select the object you want to project (use and cut the other) first then Shift select the "object to be cut". Now Tab into Edit mode and press Knife project.
Before projecting from a text object and Resulting knife projection.