Question

what is President and governors rule

Answer 1

Due to some circumstances when the government gets dissolved then in that situation the orders will be giveb by governer of state and president of nation.This is what knowb as presidents and governers rule.
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Answer 2

In India, President's rule refers to suspension of state government and imposition of directCentral Government rule in a state. UnderArticle 356 of the Constitution of India, in the event that a state government is unable to function according to constitutional provisions, the Central government can take direct control of the state machinery. Subsequently, executive authority is exercised through the centrally appointed governor, who has the authority to appoint other administrators to assist them. The administrators are usually nonpartisan retired civil servants.

When a state government is functioning correctly, it is run by an elected Council of Ministers responsible to the state's legislative assembly (Vidhan Sabha). The council is led by the Chief Minister, who is the de facto chief executive of the state; the Governor is only ade jure constitutional head. However, during President's rule, the Council of Ministers is dissolved, vacating the office of Chief Minister. Furthermore, the Vidhan Sabha is either prorogued or dissolved, necessitating a new election.

Similarly, in the state of Jammu and Kashmir, failure of governmental function results inGovernor's rule, imposed by invoking Section 92 of the Constitution of Jammu and Kashmir. The state's governor issues the proclamation, after obtaining the consent of the President of India. If it is not possible to revoke Governor's rule within six months of imposition, the President's Rule under Article 356 of the Indian Constitution is imposed. There is little practical difference between the two provisions.

Following its landmark judgment in the 1994Bommai case, the Supreme Court of India has restricted arbitrary impositions of President's rule.

Chhattisgarh and Telangana are the only states where President's rule has yet to be imposed.