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Are both sentences correct:
1.Parents' Day is on the seventh of December.
1a.The Parents' Day is on the seventh of December.
2.Mid-Autumn Festival is on the twelfth of September.
2a. The Mid-Autumn Festival is on the twelfth of September.
We rarely use the definite article with 'day'- Xmas day, Boxing Day. With 'festival' we sometimes omit it (harvest festival), but often include it- the summer festival, the village festival, etc.
"the" before specific Festivals and Days 
Linear Mode
