In Catcher in the Rye, Chapter 11 is a simple flashback of Holden's memories of time spent with Jane. At one point, Holden brings up his recollection of them playing checkers together. The checker game could be a symbol related to Holden's life. This can be explained through the motions that Holden goes through in the novel. At each turn, Holden is blocked by events that he has no control over, therefore, similar to a game of checkers.
Chapter 12's symbolism is very different. Holden has been very concerned about the ducks at the lagoon by Central Park. Here he asks a cab driver if he knows where all of the ducks go in winter. The ducks are symbolic of Holden himself.
I mean does somebody come around in a truck or something and take them away, or do they fly away by themselves?
First, the ducks are symbolic of Holden because, unconsciously, he seems to fear the inevitable (what Mr. Antoini refers to as "a special kind of fall, a horrible kind")- mental deterioration and commitment to a mental ward. This speaks to the fact that Holden believes that someone comes and gets the ducks and takes them to a place where they will live a better life.
Second, the ducks are symbolic of Holden because he also questions whether or not the ducks fly away on their own. This is something that Holden contemplates regularly- running away.