Perhaps it is the time to replace hints with direct answers to my puzzle.
First, those who misunderstood the question, or misinterpreted the implicit assumptions, or proposed some interpretations which I dismissed as invalid, did nothing wrong: it is quite usual that when a subject is discussed within a group of people unfamiliar with the implicit assumptions of the subject, all kinds of variations in the interpretation of the situation can occur, and require clarification.
Nevertheless, as the picture
https://www.physicsclassroom.com/cla...-Angle-Mirrors sent to us by Roger shows, my question makes quite straightforward practical sense and has a quite definite answer: 2 mirrors produce 3 mirror images, and not 2 how one might think.
A right way to think of mirror reflections in geometrical optics should be familiar from the story about Alice behind the looking glass. Instead of thinking that a light ray from the actual object reflects in a mirror before reaching our eye, one may equivalently think that it is the object that gets reflected in the mirror to occupy a new position behind the glass, and the light ray from that new position travels to our eye straight through the mirror surface. So, the question about the number of images becomes the question about the number of such "new positions".
In fact, if two mirrors in Roger's link were not perpendicular to each other, the number of reflections could be larger than 3 or even (theoretically speaking) infinite - depending on the angle between the mirrors. This is because one will see not only reflections of the object in each of the mirrors, but also reflections in the reflected mirrors, doubly-reflected mirrors and so on. But with the 90-degree angle there will be only 4 images (the object and 3 reflections) and with 3 pairwise perpendicular mirrors 8 (1+7).
To see why, imagine a rectangular box (to be closer to home, think of a cardboard box filled with yet unsold copies of your book). It is a very symmetric shape with 8 corners. It has 3 symmetry planes: one horizontal and two vertical (one parallel to the longer side of the box, the other parallel to the shorter side). Consider one of the 8 corners to be "the object" and start reflecting it in these 3 pairwise perpendicular symmetry planes. No matter how many times you reflect, you'll get just one of the 8 corners of the box. Looking at them from wherever you are you'll see the 8 identical images (the "actual" corner plus its 7 "reflections").
Now, let's return to the poem. In it, Dmitry Usov parallels an act of translating to reflecting in a mirror. So, as one expects, when an object (the original quatrain) is "reflected" (translated), we get two incarnations of it: the original and the translation.
But my post contains also an English translation of the poem (i.e. one more mirror), and - contrary to what one instinctively expects with two mirrors - my post contains not 3 (the source and two reflections) but 4
incarnations of the same quatrain. That was supposed to work as a hint for you (and it did work for some) that two mirrors produce not 1+2 images, but 1+3.
However, in addition to the two metaphorical mirrors (mock-translation from a language to itself, and translation between Russian and English), the poem also contains a third mirror, the looking glass through which the Moon is seen. So, if you count not how many copies of the same quatrains are there, but how many images of the Moon are mentioned there, you literally get the right answer for three mirrors: 8.
The number itself comes simply as the number of regions (they are suggestively called
octants) into which three (pairwise perpendicular) planes divide space: each region will contain one incarnation of Alice who travelled across these three mirror planes.