To save your file as separate segments, try Batch Manager.
Click on the menu: Tools>Start Batch Manger and specify your destination directory. Click "Done" to return to the main editing screen.
It is easier to use scene mode in this case.
Select "Scene Mode" and "Queue To Batch Clears Cut List" in Tools>Options>General Parameters)
Select each segment individually and add it to the Batch with Ctrl+B
Select your next segment and add to Batch with Ctrl+B
Continue until you have selected all of your segments then click Tools>Start Batch Manger and press the "Save and Execute" button. Your files will be saved as individual segments.
Before you save to batch, look at the timeline. Make sure that it is all red except for the 6 min section you want to save. Then queue to batch. Note that once you queue something to batch, it saves the cuts at the time it was queued. If you change any cuts, it does not change what has already been queued to batch.