Looks like a result of using boolean operations to model which makes a mess, and for some reason part of it is separated to another object.
- select and join the objects. ctrl+J
- select all geometry and remove doubles, W -> remove doubles
- split concave faces, mesh menu -> clean up: split concave faces
- select none, select non-manifold, ctrl+alt+shift+M
- find and fix open edges and overlapping geometry that makes the mesh non-manifold
Attaching a .blend is good. It didn’t have images packed in and the file wasn’t compressed, in case you’re assuming it would. Tutorial linked in my signature shows how to have those.
That’s not a screenshot. It’s a cropshot that hides the feedback from the interface. Don’t crop images when asking questions.
BIG SYN LOGO2.blend (94.7 KB)