The National Highways connecting Goa to other parts of India are:

NH 4A and NH 17
NH 66 and NH 166
NH 4 and NH 7
NH 1 and NH 44

The correct answer is: NH 66 and NH 166.

NH 66 is a national highway in India that runs from Surat in Gujarat to Kanyakumari in Tamil Nadu. It is one of the longest national highways in India, with a total length of 1,956 km. The highway passes through the states of Gujarat, Maharashtra, Goa, Karnataka, Kerala, and Tamil Nadu.

NH 166 is a national highway in India that runs from Panaji in Goa to Mangalore in Karnataka. It is a 140-km-long highway that passes through the states of Goa and Karnataka.

The other options are incorrect. NH 4A is a national highway in India that runs from Mumbai in Maharashtra to Panaji in Goa. It is a 584-km-long highway that passes through the states of Maharashtra and Goa. NH 17 is a national highway in India that runs from Mumbai in Maharashtra to Mangalore in Karnataka. It is a 620-km-long highway that passes through the states of Maharashtra, Goa, and Karnataka. NH 4 is a national highway in India that runs from Delhi in Delhi to Chennai in Tamil Nadu. It is a 1,394-km-long highway that passes through the states of Delhi, Haryana, Rajasthan, Gujarat, Maharashtra, Karnataka, and Tamil Nadu. NH 7 is a national highway in India that runs from Varanasi in Uttar Pradesh to Kanyakumari in Tamil Nadu. It is a 2,340-km-long highway that passes through the states of Uttar Pradesh, Madhya Pradesh, Maharashtra, Karnataka, Kerala, and Tamil Nadu. NH 1 is a national highway in India that runs from New Delhi in Delhi to Kanyakumari in Tamil Nadu. It is a 4,342-km-long highway that passes through the states of Delhi, Haryana, Rajasthan, Gujarat, Maharashtra, Karnataka, Kerala, and Tamil Nadu.