Learn English – Why do we say: “what time is it?”

The armed services (and their veterans) really have this engrained in my mind as such:

Rendezvous at 0600 [O-Six-Hundred] hours!

Drop point is X degrees north, at 1200 [Twelve-Hundred] hours!

Otherwise, where more precise in terms of declaring minutes, you can just split them and speak each unit of time individually:

Your meeting is at 1530 [Fifteen-Thirty] hours.

Your meeting is at 1812 [Eighteen-Twelve] hours.

The hours here, it might be argued, is redundant or even inaccurate, but that doesn't dictate the occurrences (or exclusion of such) in speech.

You could go the quarter to, half past route, but this is an interchangeable method of speaking time, not exclusive to verbalising time in its 24-hours form.

Since o'clock is an abbreviation of of the clock, I guess that technically you could speak in this manner in terms of 24-hours, such as: 15 o'clock. But this might sound a little peculiar to most. If we look at the definition of o'clock from TheFreeDictionary then it kind of indicates we would be playing it safer to use another form:

1. Of or according to the clock: three o'clock.

2. According to an imaginary clock dial with the observer at the center and 12 o'clock considered as straight ahead in horizontal position or straight up in vertical position. Used to indicate relative position: enemy planes at 10 o'clock.

3. used after a number from one to twelve to indicate the hour of the day or night

4. (Mathematics & Measurements / Navigation) used after a number to indicate direction or position relative to the observer, twelve o'clock being directly ahead or overhead and other positions being obtained by comparisons with a clock face

If we do decide to use the 24 o'clock approach, then it's just redundant, if nothing else; consider the note on relativity to the face / direction. Since, regardless of the numbers being bigger, we don't have to (necessarily) do any extra laps around the clock face to arrive at the specified location - but in cases where AM and PM might not be clearly implied, it could serve to do that.

The Wikipedia article 12 Hour Clock is worth quoting at length:

Confusion at noon and midnight

It is not always clear what times "12:00 a.m." and "12:00 p.m." denote. From the Latin words meridies (midday), ante (before) and post (after), the term ante meridiem (a.m.) means before midday and post meridiem (p.m.) means after midday. Since strictly speaking "noon" (midday) is neither before or after itself, the terms a.m. and p.m. do not apply. However, since 12:01 p.m. is after noon, it is common to extend this usage for 12:00 p.m. to denote noon. That leaves 12:00 a.m. to be used for midnight at the beginning of the day, continuing to 12.01 a.m. that same day.

However, because practical confusion is still possible, some style guides recommend replacing "12:00 p.m." with "12:00 noon" and "12:00 a.m." with "12:00 midnight".

The American Heritage Dictionary of the English Language (Fourth Edition, 2000) has a usage note on this topic: "Strictly speaking, 12 a.m. denotes midnight, and 12 p.m. denotes noon, but there is sufficient confusion over these uses to make it advisable to use 12 noon and 12 midnight where clarity is required."

Many U.S. style guides, and NIST's "Frequently asked questions (FAQ)" web page, recommend that it is clearest if one refers to "noon" or "12:00 noon" and "midnight" or "12:00 midnight" (rather than to "12:00 p.m." and "12:00 a.m."). Some other style guides suggest "12:00 n" for noon and "12:00 m" for midnight.

The Canadian Press Stylebook (11th Edition, 1999, page 288) says, "write noon or midnight, not 12 noon or 12 midnight." Phrases such as "12 a.m." and "12 p.m." are not mentioned at all.

The use of "12:00 midnight" or "midnight" is still problematic because it does not distinguish between the midnight at the start of a particular day and the midnight at its end. To avoid confusion and error, some U.S. style guides recommend either clarifying "midnight" with other context clues, or not referring to midnight at all. For an example of the latter method, "midnight" is replaced with "11:59 p.m." for the end of a day or "12:01 a.m." for the start of the next day. That has become common in the United States in legal contracts and for airplane, bus, or train schedules, though some schedules use other conventions.

My advice is to use "12:00 noon" instead of "12:00 p.m." and "12:00 midnight" instead of "12:00 a.m." Realize that readers may be confused which day 12:00 midnight belongs to, so make sure context makes it clear.