Answer: Nixon's goal was not to have a strong federal government, but rather to give more power to the states called New Federalism.
New Federalism: Federalism is a form of government whereby the same territory is controlled by two levels of government. An overarching national government typically governs larger territories, while smaller subdivisions, states, and cities take care of issues that are largely local. Rather than just being controlled by the government itself, Nixon hoped to spread more power throughout the states
How Nixon Worked Toward His Goal:
On October 20, 1972, President Richard Nixon declared an open attempt at reversing the flow of power from the federal government back to the states. In 1972, Nixon signed a bill that incorporated revenue sharing with the states and gave over $30 billion to state and local governments. The State and Local Fiscal Assistance Act of 1972 authorized the federal revenue-sharing (FRS) grants which were given to state and local governments over a period of four years until 1986 under President Reagan.
China has a (Socialist) government
That would be the state's supreme court or its equivalent level court in the state, that is the highest court in that particular state. The courts are divided into several layers and as such we have courts of special jurisdiction, trial courts, the appellate courts and the supreme courts. These are organized in hierarchical structure where the decisions made by the higher court effect those lower level courts. The highest court is usually the supreme court, followed by the appellate courts and the come the trial and special jurisdiction courts. So the the decision made by the appellate court would not affect only the supreme court.