Java Error: illegal start of expression

Remove the public keyword from int[] locations={1,2,3};. An access modifier isn't allowed inside a method, as its accessbility is defined by its method scope.

If your goal is to use this reference in many a method, you might want to move the declaration outside the method.

Methods can only declare local variables. That is why the compiler reports an error when you try to declare it as public.

In the case of local variables you can not use any kind of accessor (public, protected or private).

You should also know what the static keyword means. In method checkYourself, you use the Integer array locations.

The static keyword distinct the elements that are accessible with object creation. Therefore they are not part of the object itself.

public class Test { //Capitalized name for classes are used in Java
   private final init[] locations; //key final mean that, is must be assigned before object is constructed and can not be changed later. 

   public Test(int[] locations) {
      this.locations = locations;//To access to class member, when method argument has the same name use `this` key word. 
   }

   public boolean checkYourSelf(int value) { //This method is accessed only from a object.
      for(int location : locations) {
         if(location == value) {
            return true; //When you use key word return insied of loop you exit from it. In this case you exit also from whole method.
         }
      }
      return false; //Method should be simple and perform one task. So you can get more flexibility. 
   }
   public static int[] locations = {1,2,3};//This is static array that is not part of object, but can be used in it. 

   public static void main(String[] args) { //This is declaration of public method that is not part of create object. It can be accessed from every place.
      Test test = new Test(Test.locations); //We declare variable test, and create new instance (object) of class Test.  
      String result;
      if(test.checkYourSelf(2)) {//We moved outside the string
        result = "Hurray";        
      } else {
        result = "Try again"
      }
      System.out.println(result); //We have only one place where write is done. Easy to change in future.
   } 
}