It is implied that the person told his case to Absalom. This can be stated clearly. Alternate translation: "Absalom would ask him what his problem was, and the man would then explain to Absalom why he sought justice. Absalom would then say to him" (See: [[rc://en/ta/man/translate/figs-explicit]])
"Hearing" a case means to listen to it and to make a judgement decision over it. Alternate translation: "to judge your case" or "to oversee your case" (See: [[rc://en/ta/man/translate/figs-metonymy]])