12/24h Time format converter
General comments:


try to indent your code properly - it is hard to read at the moment
follow the language conventions: variable should start in lower case (Hour24 => hour24)
similarly, opening braces are at the end of the line, not at the beginning of a new line (like in C-like languages)
try to do only one thing in one method - at the moment your methods do the conversion and print at the same time


Regarding your question about efficiency - a more efficient way (less time to code and fewer lines of code) would be to use existing libraries.

With Java 8, you could use the java.time API:

private static final DateTimeFormatter FMT_24 = DateTimeFormatter.ofPattern("HH:mm:ss");
private static final DateTimeFormatter FMT_12 = DateTimeFormatter.ofPattern("h:mm:ssa");

public static String convertTimeTo24(String time12) {
  LocalTime time = LocalTime.parse(time12, FMT_12);
  return FMT_24.format(time);
}

public static String convertTimeTo12(String time24) {
  LocalTime time = LocalTime.parse(time24, FMT_24);
  return FMT_12.format(time);
}


And to avoid duplicating code, you could refactor the two methods into:

public static String convertTimeTo24(String time12) {
  return convertFormats(time12, FMT_12, FMT_24);
}

public static String convertTimeTo12(String time24) {
  return convertFormats(time24, FMT_24, FMT_12);
}

private static String convertFormats(String fromTime, DateTimeFormatter fromFormat,
                                                      DateTimeFormatter toFormat) {
  LocalTime time = LocalTime.parse(fromTime, fromFormat);
  return toFormat.format(time);
}


Your main method needs to be changed accordingly.