Paul speaks of the law here as if it were alive and had its own voice. AT: "everything that the law says people should do is for" or "all the commands that Moses wrote in the law are for" (See: [[rc://en/ta/man/translate/figs-personification]])
Here "mouth" is a synecdoche that means the words people speak. You can translate this in an active form. AT: "so that no people will be able to say anything valid to defend themselves" (See: [[rc://en/ta/man/translate/figs-synecdoche]] and [[rc://en/ta/man/translate/figs-activepassive]])
Here "world" is a synecdoche that represents all the people who live in the world. AT: "that God can declare everyone in the world guilty!" (See: [[rc://en/ta/man/translate/figs-synecdoche]])