On February 4th, 1981, Ronald Reagan walked into his first Cabinet meeting as President, waited for silence, uttered these words, and then walked out of the room. He was successful on all three of these goals.
Regarding inflation, the CPI stood at 11.83% in January of 1981, the month Reagan took office. When he left office in January of 1989, the CPI was down to 4.67%.
Regarding taxes, the record is nuanced, with some taxes being lowered on his watch and others being raised. However, overall taxes fell from 18.9% of GNP to 18.3% of GNP.
Regarding communism, during the Reagan administration, the Berlin Wall fell and the Soviet Union began to crumble. Whereas some of his peers and predecessors believed either that the United States could coexist with the Soviet Union, that the threat from the Soviet Union would pass, or that the two superpowers were morally equivalent, Ronald Reagan wanted to defeat the Soviet Union, which was succinctly expressed by his Cold War strategy: "We win, they lose". His strategy had many prongs. His administration persuaded Saudi Arabia to increase their production of oil (and hence lower the price) to cut off the revenue the USSR received from its sale of this commodity. His administration helped arm the mujahedeen in Afghanistan who were fighting the Soviets. Broadcasts were supported that preached to Muslims the incompatibly of their faith with communism. The Reagan Administration provided Solidarity, the trade union in Poland that resisted the Soviets, with radios and communication equipment. Reagan supported a strong national defense and pursued the Strategic Defense Initiative (SDI). Perhaps most of all, he used the bully pulpit to speak out against communism and declared the Soviet Union and Evil Empire, providing hope, encouragement, and moral support to the millions of people who struggled under its jackboot and fought for their freedom.
It is not true that the Berlin Wall fell during the Reagan administration. Reagan left office in January 1989, whereas the Wall fell on November 9 that year; see http://en.wikipedia.org/wiki/Berlin_Wall#The_Fall .