The Mandovi River originates in the Western Ghats of:

Karnataka
Maharashtra
Kerala
Tamil Nadu

The correct answer is Karnataka.

The Mandovi River is a river in the Indian state of Goa. It originates in the Western Ghats near the village of Mollem in the Sattari taluka of North Goa district. The river flows south through the state, passing through the cities of Panaji and Margao, before emptying into the Arabian Sea at the Mandovi estuary. The Mandovi is the largest river in Goa and is a major source of water for irrigation and drinking water. The river is also a popular tourist destination, with many beaches and resorts located along its banks.

The other options are incorrect. Maharashtra is a state in western India. Kerala is a state in south-west India. Tamil Nadu is a state in south India.