The correct answer to the question is option 3, Narmada. The Narmada river flows between the Satpura and Vindhya ranges. The Satpura Range is located in central India, while the Vindhya Range stretches across central and western India. The Narmada river originates in the Amarkantak hills in Madhya Pradesh and flows westward through the states of Madhya Pradesh, Maharashtra, and Gujarat before emptying into the Arabian Sea.

Option 1, Tapi, is incorrect as it flows through the states of Maharashtra and Gujarat but does not pass between the Satpura and Vindhya ranges. Option 2, Sabarmati, is also incorrect as it flows through the state of Gujarat and does not pass between these ranges. Option 4, Mahi, is incorrect as it flows through Gujarat but is not located between the Satpura and Vindhya ranges.

Therefore, the Narmada river is the correct answer to the question.