This figure of speech comes from giving something a proper burial.  In the USA, grave is at least 6 feet deep.  At sea, ‘proper’ burial would be 6 fathoms (a fathom is water 6 feet deep; so, 6 fathoms = 36 feet).  In common usage, giving something ‘the deep six’ means to cancel plans, or to stop a project.  ‘I gave it the deep six’.