I have an image which I traced, optimized and want to cut out using a laser engraver.  I need to join a couple of placed together so that they become one  (it's a kind of lettering and two of the letters are separate) .  I cannot seem to get the nodes to join to provide me with one complete item.

I know I am doing something wrong - but I don't know what.  Thank you to anyone who can help, I can upload the original file if required or here is an example from Paint.

Use outline display mode to see where paths are interrupted or not.

Here, probably, you have to break right (sub?) path between the two right nodes you pointed, break left (sub) path between the two left nodes you pointed, then you'll be able to join the two bottom nodes and the two upper nodes.

In this scenario, you may need to disconnect the right sub-path between the two right nodes and the left sub-path between the two left nodes. This action should enable you to connect the two bottom nodes and the two upper nodes seamlessly.

Maybe like so after combining paths:

Polygon perfectly illustrated the way to do. 

I'd add : you are not obliged to combine the two paths if not already done : when joining the nodes, they will be automatically combined. Depending on your goal you can also fuse nodes into one (Join selected nodes : the first icon from the left on Polygon's gif) or create a segment joining the two nodes, as does Polygon.