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The nut broke off and had a small red ring/gasket between these connectors. I'm an noob but can follow instructions. Please give suggestions. Thanks
Below there is a water valve 
which may be used as an alternative if the above (cupper?) pipe is inconvenient to use.
Oof. No simple replacement nut to toss on there, unfortunately.
What i'd do if it were mine:
hacksaw and careful cutting of the copper a couple inches above the valve to get rid of the copper tubing (nothing wrong with copper, just harder to work with)
fitting on the end of the copper to give it a usable end. Easiest would be a threaded hose connection, something like this
that lets one put a common washing machine hose from the end to the appliance. Flexible hoses reduce trouble from the machine being moved a little by people/vibration.
You should not use a hacksaw to cut copper pipe for a sharkbite fitting, because supposedly the main thing that causes those to fail is the rubber o ring being damaged from rough edges. It's worth paying the $20 for a pipe cutter to not have to worry about a leak.