Local self-government can be best explained as an exercise in

Answer

Democratic decentralization

(a) Federalism: Federalism means constitutional division of powers between Union and States. Local bodies are below the State level, so this is not the best explanation.
(b) Democratic decentralization: Local self-government means transfer of power, functions and participation to elected bodies at the local level. This is the correct concept.
(c) Administrative delegation: Delegation is only transfer of administrative authority from higher to lower officials, usually without autonomous self-rule. Local self-government is more than delegation.
(d) Direct democracy: Direct democracy means people decide issues themselves without representatives, as in referendums or gram sabha-type elements. Local self-government mainly works through elected representatives, so this is not the best answer.