Things could have different meaning for different people
The fence
"the other side of the fence"
the fence where they would meet
the lesson and the mark
The phrase "the other side of the fence" basically means that one side is different than another.
In the story, the phase is proven to be true as the Mukakas, or the neighbors was hinted to be more privileged than Matteu when he noted that "he was strict with us, but he behaved differently with Mr Mukuka". This shows that each family have a very different situation
A fence's purpose is too separate things, but instead, in the story, Matteu uses it to connect him and his new friends, which proves that things could have multiple meanings.
In the story, the main meeting place for when they would play is at the fence right under the tree.
The tree
The neighbors
Lesson
Lesson
Mark
Mark
The lesson from the tree is to probably
be more careful, or to not climb at all
The mark from the tree was a physical
scar from when he fell from the tree
The lesson he got from the neighbors was the difference between his family and the Mukakas.
The mark that he received from his neighbors was intangible, where he finally understood his family's roles in life
All of these possibilities is a representation of how double meaning is used throughout the book