When the watch showed 9:14, the minute hand points to `2` (that is, minute 14), and the hour hand points slightly beyond `9`. If positions of the hour and minute hands are interchanged, the `2` position which was occupied by the minute hand before, is now occupied by the hour-hand and the `9+` position, previously occupied by the hour hand is now occupied by a minute hand. This interprets the time as almost `3` hour and some minutes near `45` (as 9+ is closer to `45` in minute terms).

We can not be exactly sure that it`s 45 minutes, it`s slightly less. Thus, it tells us it`s closer to option `2` (13 minutes to three) or `3` (14 minutes to three). Given the correct answer is `3` (fourteen minutes to three), we can assume it must`ve been slightly closer to 14 than to 13 minutes past the hour.