Final answer:
The nationalist/self-determination organization formed in Israel in the 1960s was the Palestine Liberation Organization (PLO), which was aimed at creating a homeland for Palestinians and is now recognized by the United Nations.
Step-by-step explanation:
The nationalist/self-determination organization formed in Israel in the 1960s is the Palestine Liberation Organization (PLO). The PLO was established in 1964 with the aim of creating a homeland for the Palestinian people. Initially, it sought the elimination of the state of Israel, which led to it being considered a terrorist organization by many, especially during the 1970s because of violent attacks committed against Israel and Israelis. Over the years, the PLO has evolved, and while it still remains dedicated to the creation of a Palestinian homeland, it has officially recognized Israel and its right to exist peacefully. This reinvention has led to recognition by the United Nations, though the PLO's image as a terrorist organization persists among some groups, notably in the United States.