Final answer:
The correct answer is option a.) used to keep lunar calendars approximately synchronized with solar calendars.
Step-by-step explanation:
The Metonic cycle is used to keep lunar calendars approximately synchronized with solar calendars. This cycle was recognized by the ancient Greek astronomer Meton, who observed that after 19 years, the phases of the moon repeat on the same days of the year, or nearly so.
The Metonic cycle is based on the fact that 19 solar years are pretty close to 235 lunar months, which makes the average year length 365.24 days when following this system. The Metonic cycle is more accurate than the Julian calendar but less so than the Gregorian calendar. It is used by Jews for their religious calendar and was likely invented by the ancient Babylonians, influencing other calendar systems, such as the traditional Chinese calendar.