Error message when I go to verify (error: expected ')' before ';' token)

error: expected ')' before ';' token

This is the error code I get when I go to compile. Here is my code, I am programming an LED to turn on for .5 seconds, then to turn on for 2 seconds.

#include <stdio.h> 
void setup() {
  
  pinMode(LED_BUILTIN, OUTPUT);
  
}

void loop() {
  int x;
  
  while(x=0;x<4;x++;){
    digitalWrite(LED_BUILTIN, HIGH);
    delay(500);  
    }
    
  while(x=0;x<4;x++){ 
  digitalWrite(LED_BUILTIN, LOW);
  delay(2000);
  }
  
}

Where did you get the idea that is the way to write a WHILE loop? ? ?

Anyway, the IDE displays where in your code occurs if you look at it.
Black box (lower box of the IDE).

Here is a screenshot of all the error messages.

We don't need a screenshot of the errors.
You need to go away and look at the syntax of a while loop (you probably meant to use a for loop )

Reconfirming the comments above, the issue resides in your use of the "while" condition; the condition referenced can be true or false.

example:
int x;
while (x < 5){
x++;
}

Anyhow, obviously you're new and trying figure out and build a foundation of learning; below is the only code you need:

void setup() {
  pinMode(LED_BUILTIN, OUTPUT);
}

void loop() {
  digitalWrite(LED_BUILTIN, HIGH);
  delay(500);  

  digitalWrite(LED_BUILTIN, LOW);
  delay(2000);
}