Correct answer:
<h2>Reducing national authority over state governments.</h2>
Additional historical details:
In his campaign for the presidency in 1980, Ronald Reagan promised to decrease taxes and reduce the size of the federal government. He also promised to improve the economy, restore faith in the nation, and make the US military stronger.
In his inaugural address in 1981, Reagan said, "Government is not the solution to our problem; government is the problem." He talked much about lowering taxes and reducing the role the federal government played in solving people's problems. As noted in the part of the speech quoted in the question, he promised to give more authority to the states and people locally.
As for curbing the size and influence of the federal establishment, Reagan did push for huge tax cuts in 1981 ... but then the government deficit soared and Congress (with President Reagan's signature) passed laws raising taxes again in 1982, 1983, 1984 and 1987 -- undoing much of the original tax cutting that had been done in 1981.
While Pres. Reagan talked about smaller government, federal government expenditure got bigger during Reagan's presidency, as it did under all presidencies in the second half of the 20th century. It's hard to promise smaller government and at the same time increase military spending (which was a Reagan priority). Federal government spending has gone up by about 2.3% (on average) under all presidents since World War II. It just depended on what programs they spent their money on. For Reagan, the priority was military spending and having a forceful foreign policy in international affairs.
