Use a recursive query for this:
--Prepare Dummy Data
;WITH CITIES 
     AS (SELECT 100   AS City_Code, 
                'A1'  AS Post_code, 
                'ABC' AS Post_Code_Description 
         UNION 
         SELECT 100   AS City_Code, 
                'C8'  AS Post_code, 
                'XYZ' AS Post_Code_Description 
         UNION 
         SELECT 100   AS City_Code, 
                'Z3'  AS Post_code, 
                'MNO' AS Post_Code_Description 
         UNION 
         SELECT 200   AS City_Code, 
                'D4'  AS Post_code, 
                'LMN' AS Post_Code_Description 
         UNION 
         SELECT 300   AS City_Code, 
                'E3'  AS Post_code, 
                'IJK' AS Post_Code_Description 
         UNION 
         SELECT 300   AS City_Code, 
                'B9'  AS Post_code, 
                'RST' AS Post_Code_Description), 
--Add Row numbers to each row
     PREPARE 
     AS (SELECT *, 
                ROW_NUMBER () 
                  OVER ( 
                    PARTITION BY CITY_CODE 
                    ORDER BY CITY_CODE) RN 
         FROM   CITIES),
--Start Recursive CTE 
     RECURSIVE 
     AS (
--Anchor Query
         SELECT CITY_CODE, 
                CAST(POST_CODE AS VARCHAR(MAX))             Post_code, 
                CAST(POST_CODE_DESCRIPTION AS VARCHAR(MAX)) 
                Post_Code_Description, 
                1                                           AS LEVEL, 
                RN 
         FROM   PREPARE 
         WHERE  RN = 1 
         UNION ALL 
--Recursive Query
         SELECT T1.CITY_CODE, 
                T1.POST_CODE + ',' + T2.POST_CODE, 
                T1.POST_CODE_DESCRIPTION + ',' 
                + T2.POST_CODE_DESCRIPTION, 
                T2.LEVEL + 1, 
                T1.RN 
         FROM   PREPARE AS T1 
                INNER JOIN RECURSIVE AS T2 
                        ON T1.RN = T2.RN + 1 
                           AND T1.CITY_CODE = T2.CITY_CODE) 
--Final Results
SELECT T1.CITY_CODE, 
       T1.POST_CODE, 
       T1.POST_CODE_DESCRIPTION 
FROM   RECURSIVE T1 
       INNER JOIN (SELECT CITY_CODE, 
                          COUNT(*) cnt 
                   FROM   CITIES 
                   GROUP  BY CITY_CODE)T2 
               ON T1.CITY_CODE = T2.CITY_CODE 
WHERE  T1.LEVEL = T2.CNT