By the facts you have provided it is clear that your father asked you to tell total distance I.e 3+3=6kms but you started from home and again came back home so,the total displacement will be 0 since displacement= distance between initial and final point so your father must have asked your bro about the displacement of you journey that it.
As u both went to park from home and returned back to home,so ur bro said that he walked for 6 Kms where as u said that 0,Actually ur bro means that ur distance covered is 6 Kms(3Kms from home to park and 3 from park to home)Whereas u returned home so that means ur displacement was 0 bcoz u both returned home from park.