The National Highways (NH) network in India is an extensive road network connecting various states and cities across the country. To determine which National Highway passes through Maharashtra, Chhattisgarh, and Odisha (formerly known as Orissa), we need to analyze the options provided.

Option 1: NH4

National Highway 4 (NH4) is an important highway in India, connecting the states of Maharashtra, Karnataka, Tamil Nadu, and Andhra Pradesh. However, it does not pass through Chhattisgarh or Odisha. Therefore, NH4 is not the correct answer.

Option 2: NH5

National Highway 5 (NH5) is a significant highway that stretches from Chennai in Tamil Nadu to Kolkata in West Bengal. It passes through the states of Andhra Pradesh and Odisha, but it does not pass through Maharashtra or Chhattisgarh. Hence, NH5 is not the correct answer.

Option 3: NH6

National Highway 6 (NH6) is a major highway in India that runs from Hazira in Gujarat to Kolkata in West Bengal. NH6 is the correct answer to the question because it passes through the states of Maharashtra, Chhattisgarh, and Odisha. It connects Nagpur, Raipur, and Sambalpur, among other significant cities in these states.

Option 4: NH7

National Highway 7 (NH7) is a crucial highway in India, connecting Varanasi in Uttar Pradesh to Kanyakumari in Tamil Nadu. While NH7 passes through Maharashtra and Chhattisgarh, it does not extend to Odisha. Thus, NH7 is not the correct answer.

In summary, the National Highway that passes through Maharashtra, Chhattisgarh, and Odisha is NH6 (Option 3). It serves as a vital transportation route connecting these three states and facilitating the movement of goods and people across the region.