I'm making some bangs for my new hair mesh by editing and enlarging the existing bangs. What I'd like to do is disconnect the bangs from the bottom of the hair, so they're more free hanging. But I can't figure out how to disconnect these two sets of vertix. I've read over the tutorials, and but I didn't find where it said how to do that. The four points I want to disconnect are in red on the attached picture. This is a picture of the hair I'm trying to reproduce If anyone has any suggestions on how to do it, it'd be helpful.

It looks like you have four vertices selected which also attach to the base and upper part. You need those vertices to stay because they are used by other faces.
Try changing to select by face, select the triangles and delete them one at a time. The vertices will remain attached to the other faces because they are shared.

How do you select the triangles?

Change the program to select by face instead of vertex. It's on the screen when you see select. You might try doing some generic milkshape tutorials in order to learn your way around the program.