Arduino Nano, DS3231 RTC clock module and 4 cascaded FC-16 led matrix modules
how do I display the time from the DS3231 clock module on the FC-16
  led matrix modules?


You can use the DateTime::toString() method to convert the
current time to a string in the format of your choice, then P.print()
to display that string on the LED matrix:

void loop() {
    DateTime now = rtc.now();
    char buffer[] = "hh:mm";  // hours and minutes
    P.print(now.toString(buffer));  // display
}



  how do I use that hour of the day so that the microcontroller knows
  what text it should display next?


Condition your logic on now.hour().