Please read the README in front of this code.

gistfile1.txt

/*
README:
Updated on 13/Oct. I can use self.favoriteList in .m file. Then we can use custom getter here.

1. The implemetation I did for the first time was correct. I used "@property (atomic) NSMutableArray<NSString *> *favoriteList;" in @interface Booking() and it works.
2. I don't need "//@synthesize favoriteList = _favoriteList;" for creating setter and getter, becuase Xcode will create them automaticlly now.
3. I think my implementation is better than having a "@property (atomic) NSMutableArray<NSString *> *favoriteList2;" in .m. Becuase having a favoriteList2 may confuse people. The cons of my implementation is that you may create custom getter and setter so you don't want to use _favoriteList, but for this simple example it should be fine.
*/

//
//  Booking.h
//  test
//
//  Created by allenlinli on 10/11/16.
//  Copyright © 2016 Raccoonism. All rights reserved.
//

#import <Foundation/Foundation.h>

@interface Booking : NSObject
@property (atomic, readonly) NSArray *favoriteList;
- (void)addFavorite:(NSString *)cityName;

@end

//
//  Booking.m
//  test
//
//  Created by allenlinli on 10/11/16.
//  Copyright © 2016 Raccoonism. All rights reserved.
//

#import "Booking.h"

@interface Booking()
@property (atomic) NSMutableArray<NSString *> *favoriteList;

// Li Lin: I don't need to use favoriteList2 for implementing this functionality.
//@property (atomic) NSMutableArray<NSString *> *favoriteList2;
@end

@implementation Booking

- (instancetype)init {
    self = [super init];
    
    if (self) {
//        [self setFavoriteList: [[NSMutableArray alloc] init]];
        _favoriteList = [[NSMutableArray alloc] init];
    }
    
    return self;
}


//- (NSMutableArray *)favoriteList {
//    if (!_favoriteList) {
//        _favoriteList = [[NSMutableArray alloc] init];
//    }
//    
//    return _favoriteList;
//}
//
//- (void)setFavoriteList:(NSMutableArray *)favoriteList {
//    self.favoriteList = favoriteList;
//}

- (void)addFavorite:(NSString *)cityName {
//    [_favoriteList addObject:cityName];
    [self.favoriteList addObject:cityName];
}

// Li Lin: "synthesize" is automatically produced
//@synthesize favoriteList = _favoriteList;
@end


/*

#import <UIKit/UIKit.h>

@interface ViewController : UIViewController
@end





//
//  ViewController.m
//  test
//
//  Created by allenlinli on 10/11/16.
//  Copyright © 2016 Raccoonism. All rights reserved.
//

#import "ViewController.h"
#import "Booking.h"

@interface ViewController ()

@end

@implementation ViewController

- (void)viewDidLoad {
    [super viewDidLoad];
    
    Booking *book = [[Booking alloc] init];
    [book addFavorite:@"Seoul"];
    [book addFavorite:@"Taipei"];
    [book addFavorite:@"Darwin"];
    
//    book.favoriteList = nil;
    
    for (NSString *city in book.favoriteList) {
        NSLog(@"city:%@",city);
    }
    
}

@end

*/

Updated on 13/Oct. I can use self.favoriteList in .m file. Then we can use custom getter here.