The passage is set in the context of 1987, when Yasuhiro Nakasone was stepping down as Prime Minister of Japan after serving for an unusually long five years.
He resigned after failing to pass a 5% indirect tax bill through the Diet, despite his party’s majority.
Option (a) Eisaku Sato — was a much earlier Prime Minister (1960s–1970s) and not the most recent one at the time.
Option (c) Shintaro Abe and Option (d) Kiichi Miyazawa — were contenders for the leadership but had not been Prime Ministers before Takeshita’s succession.
Thus, the correct answer is (b).