After Section VII's analysis, necessity simply means constant conjunction and the expectation it produces in the mind. On this definition, human actions are perfectly necessary: motives reliably produce actions; character reliably produces motives. We predict human behaviour using the same inductive habits we apply to billiard balls or weather. There is no special exemption for persons.
Liberty does not mean freedom from causation — that would simply be randomness, which no one wants and which would make moral responsibility impossible. Liberty means acting in accordance with the determinations of the will, without external physical constraint. A person who acts from their own desires and character, uncoerced, is free in every sense that matters.
Hume's compatibilism rescues moral responsibility from both horns of the dilemma. If actions are caused by character, then praise and blame make sense: we are responding to the stable qualities of a person. If actions were uncaused — genuinely random — praise and blame would be absurd, since the action would bear no relation to who the person is. Necessity, far from undermining morality, is its precondition.
Section VIII of the Enquiry offers the first clearly compatibilist account of free will in the modern tradition. Hume's position — that liberty and necessity are not only compatible but mutually required — has been enormously influential in philosophy of action.