Accepting an obligation is a metaphor for agreeing with the obligation. The abstract noun "obligation" can be expressed with the verb "obligate." Alternate translation: "The Jews agreed and said that they and their descendants were obligated to celebrate the days of Purim" (See: [[rc://en/ta/man/translate/figs-metaphor]] and [[rc://en/ta/man/translate/figs-abstractnouns]])
Accepting times of fasting and lamenting is a metaphor for agreeing to fast and lament at certain times. Alternate translation: "they agreed to fast and lament at certain times" (See: [[rc://en/ta/man/translate/figs-metaphor]])