conversion from 'char' to 'String' is ambiguous

Hello I am using Arduino Uno and I have a problem statement as follows:

Write a sketch that allows a user to access data in EEPROM using the serial monitor. In the serial monitor, the user should be able to type one of two commands: “read” and “write. “Read” takes one argument, an EEPROM address. “Write” takes two arguments, an EEPROM address, and a value.

For example, if the user types “read 3” then the contents of EEPROM address 3 should be printed to the serial monitor. If the user types “write 3 10” then the value 10 should be written into address 3 of the EEPROM.

I have written the following code:

#include <EEPROM.h>

void setup() {
  // put your setup code here, to run once:
Serial.begin(9600);
int x = 0;    // This defines the adress of EEPROM
byte y;    // This defines the Data to write in the EEPROM
}

void loop() {
  // put your main code here, to run repeatedly:
String buffer = ('\0');
buffer = Serial.readString();
if (buffer.startsWith("read"))
{
  x = buffer.substring(buffer.indexOf('\0')+1.toInt());
  Serial.print("Ready to read from x:");
  Serial.print("address");
  Serial.println();
  Serial.println("EEPROM.read(x)");
}
else if(buffer.startsWith("Write")
{
x=(buffer.substring(12,9).toInt());
y=(buffer.substring(9).toInt());
Serial.print("Ready to Write");
Serial.print("y");
Serial.println();
Serial.print("To x");
Serial.print("x");
Serial.println();
EEPROM.write(x,y);
  }

}
String buffer = ('\0');

'\0' is not a String

You are confusing zero termination of C style strings (lowercase s) with the use of Strings (uppercase s)

You also need to read up on ‘variable scope’.

E.g. your variable x is declared in setup() and will not be known in loop().

You can move that declaration to loop() or you can make it global by moving it to before setup().