Final answer:
Richard Nixon's 1968 presidential campaign position was marked by a commitment to 'law and order', a plan called 'Vietnamization' to end the Vietnam War, and a focus on appealing to a new constituency through moderate policies and foreign relations progress.
Step-by-step explanation:
The position of the “new Nixon” of 1968 was as the Republican frontrunner in the presidential election, shaped by Nixon's appeal to mainstream America, his promises of law and order, and his strategy for an honorable resolution of the Vietnam War, termed “Vietnamization.” Richard Nixon catered to a new Republican constituency composed of moderate Southerners, northern blue-collar workers, and those disillusioned with the Democratic Party's stance on various social issues. During his first term, Nixon focused on slowing the progress of civil rights to appease certain voter bases and sought to bring about economic stability amidst troubles with inflation and unemployment. He achieved substantial progress in foreign policy with approaches like establishing diplomatic relations with China and entering into a policy of détente with the Soviet Union.