Father's Day
Father's Day was not celebrated in the US, outside Catholic traditions, until the 20th century. As a civic celebration in the US, it was inaugurated in the early 20th century to complement Mother's Day by celebrating fathers and male parenting.
After Anna Jarvis' successful promotion of Mother's Day in Grafton, West Virginia, the first observance of a "Father's Day" was held on July 5, 1908, in Fairmont, West Virginia, in the Williams Memorial Methodist Episcopal Church South, now known as Central United Methodist Church. Grace Golden Clayton was mourning the loss of her father, when in December 1907, the Monongah Mining Disaster in nearby Monongah killed 361 men, 250 of them fathers, leaving around a thousand fatherless children. Clayton suggested that her pastor Robert Thomas Webb honor all those fathers.
Farmers' Day
Farmers' Day or National Farmer's Day is a public holiday. It is observed on December 23 in India and October 12 in the United States of America. 
In America, it is observed on 12 October every year. It is celebrated to pay tribute to all farmers throughout American history.
The National Farmers' Day in Ghana is an annual celebration of farmers and fishermen, observed on the first Friday of December. On the occation of Farmers' Day, the Ministry of Food and Agriculture (Ghana) honors with special awards to deserving farmers and fishermen based on their practices and output. 
The National Farmer's Day in India is also known as Kisan Divas in Hindi. Farmer's Day is celebrated every year on 23 December, on the birthday of the 5th Prime Minister of India, Choudhary Charan Singh, also a farmer's leader, who introduced many policies to improve the lives of the Indian farmers. It is celebrated by organising various programs, debates, seminars, quiz competitions, discussions, workshops, exhibitions, essays writing competitions and functions.