Albert Barnes on Acts 19:38

Have a matter against any man. Have a complaint of injury; if injustice has been done them by any one.

The law is open. See the margin. αγοραιοιαγονται, i.e. ημεραι. There are court days; days which are open, or appointed for judicial trials, where such matters can be determined in a proper manner. Perhaps the courts were then held, and the matter might be immediately determined.

And there are deputies. Roman proconsuls. Acts 13:7. The cause might be brought before them with the certainty that it might be heard and decided. The Syriac reads this in the singular number--"Lo, the proconsul is in the city."

Let them implead one another. Let them accuse each other in the court; i.e., let them defend their own cause, and arraign one another. The laws are equal, and impartial justice will be done.

(+) "craftsmen" "workmen" (2) "the law is open" "the court days are kept" (++) "implead" "summon"