The passage states that Emperor Hirohito had been on the Chrysanthemum Throne for 61 years.
Since the context of the passage is around 1987 (when Noboru Takeshita was about to become Prime Minister), subtracting 61 years from 1987 gives 1926 as the year he ascended the throne.
Option (a) 1946 — incorrect; by that year, Hirohito had already been Emperor for 20 years.
Option (c) early fifties — incorrect; this is far too late compared to the actual figure.
Option (d) 1936 — also incorrect; this would make his reign only about 51 years by 1987.
Therefore, (b) is the correct answer.