Introduction:
According to the Constitution of India, the establishment of a new All India Service can be initiated through various means. One of these means is through the Rajya Sabha, which is the upper house of the Parliament of India. This option is considered correct because it aligns with the provisions mentioned in the Constitution.

Explanation:
The All India Services are prestigious civil services of the Government of India, which include the Indian Administrative Service (IAS), Indian Police Service (IPS), and Indian Forest Service (IFS). These services are responsible for maintaining administrative continuity and efficiency throughout the country.

The Constitution of India provides for the establishment of new All India Services under Article 312. According to this article, if Rajya Sabha passes a resolution by a majority of not less than two-thirds of the members present and voting, declaring that it is necessary or expedient in the national interest to establish a new All India Service, then the Parliament may by law provide for the establishment of such service.

Other Options:
Let's analyze the other options given in the question and why they are not correct:

a) More than two-thirds of the States: While the states have a significant role in the establishment of All India Services, the Constitution does not specifically mention that more than two-thirds of the states are required to initiate the establishment of a new service. The provision for initiating the establishment lies with the Rajya Sabha.

b) The Inter-State Council: The Inter-State Council is a constitutional body established to facilitate coordination and cooperation between the states and the center. However, it does not have the power to initiate the establishment of a new All India Service.

c) The Lok Sabha: The Lok Sabha, which is the lower house of the Parliament, does not have the power to initiate the establishment of a new All India Service. The power lies with the Rajya Sabha as per the provisions of the Constitution.

Conclusion:
In conclusion, according to the Constitution of India, the establishment of a new All India Service can be initiated with the initiative taken by the Rajya Sabha. The Rajya Sabha, through a resolution passed by a majority of not less than two-thirds of the members present and voting, can declare the necessity or expediency of establishing a new service. This provision ensures that the establishment of new All India Services is carried out in the national interest and with the consent of the upper house of the Parliament.