The picture you probably are looking for is not here.
I was notified in 11/2015 that a drawing in Pinterest is linked to my blog. The drawing has not been on my blog, however, because it is not my habit to upload other people's photos/pictures on my blog/website. I do use links sometimes, though. I don't know, unfortunately, who made that drawing (thumb with loops and Us and Os), but I have a vague feeling I have seen that drawing in (possibly) a German website years ago. If anyone happens to know who made the drawing, it would be nice to be able to give credit to him/her.
In autumn 2009 I went to a nalbinding course where the teacher showed us how to do the Finnish Stitch UUOO/UUOOO (flat, without thumb), and the Finnish Stitch UUOOO/UUUOOO (with thumb loops).
** At this point I have to remind that there is no one and only The Finnish Stitch, but several versions. There have been local variations, and people have also chosen a different stitch variant for different yarn thicknesses, and for different purposes. The most typical one is probably "suomeksi 2+2", ie Finnish Stitch UUOO/UUOOO.
I had learnt nalbinding from Krista Vajanto's videos first, and later from other videos, too. On that nalbinding course last autumn I learnt a third way to use the thumb.
In Vajanto's videos all the thumb loops are kept wrapped around the thumb, and the oldest thumb loop is picked up with a needle at the beginning of each stitch. A way which is described also in some of the answers of a nalbinding survey made in 1950's.
In many other videos there is only one thumb loop wrapped around the thumb, and that loop is "dropped off" or "lifted off" (depends on how you think it ;) ) onto the tip of the thumb quite at the end of each stitch. That is, first the needle is pushed under the thumb loop and the under the needle yarn (or over it, in some cases), then the thumb loop is dropped off onto the tip of the thumb, and a new thumb loop is tensioned around the thumb.
A difference between these "other videos" and Vajanto's videos is also the fact that Vajanto uses several thumb loops wrapped around the thumb. Naturally it is easier simply to drop off the one and only thumb loop than the oldest thumb loop of two or three thumb loops, though that can be done, too.
Well, on this nalbinding course we learnt yet another way! This third way to use thumb in nalbinding felt a bit akward for me, like cranking to and fro, and stubbornly I nalbound my course item, a pair of mittens, in a way I had previously learnt ;)
Later on I have ran into this same "Drop & Pick" technique both in Irma Korhonen's Degree Work "Kinnasneulatekniikka pyöräyttäen" (1981) (~ "nalbinding with turning stitch"), and in a Swedish book "Söma, nåla, binda – Nålbundet från Uppland", by Linnéa Rothquist Ericsson et al (2003). Korhonen shows Turning Stitch UUOO Down U/O Up UUOOO (under 2, over 2, pick 1 small loop from back to front, turn the tip of the needle to 3 o'clock, then return: under 2, over 3), and in Rothquist Ericsson's book there are two stitches made with this "Drop & Pick" technique. I recognize them as versions of Finnish Stitch, UUUOO/UUOOOO and UUUOOO/UUUOOOO, but in the Swedish book they naturally have local, Swedish names.
In "Drop & Pick" technique all the thumb loops, whether two or three (or even four) ones, are dropped off the thumb at the end of the stitch. First you push the needle under the thumb loops and under the needle yarn, then drop off all the thumb loops, and tension a new thumb loop. Now you need to pick up back to the thumb the same thumb loops minus one. That is, if you dropped off three thumb loops, you pick up two of them, and let them stay wrapped around your thumb.
This "Drop & Pick" technique takes more time, it seems to me, than the two other, aforementioned ways – ie. either all the thumb loops wrapped around the thumb, and the oldest one is picked up with a needle, or, the one and only thumb loop is dropped off at the end of each stitch. Though, "Drop & Pick" technique has been in use, obviously, because it can be found in different sources.
In Rothquist Ericsson's book they do not tell, unfortunately, age of those two original mittens made in "Drop & Pick" technique.
Irma Korhonen had learnt the Turning Stitch and "Drop & Pick" technique from Sylvi Ahokas who had learnt it from her grandmother at 10 years of age. Ahokas comes from the Carelian area which belongs to Russia since WWII, from Kurkijoki, which was next to municipalities of Parikkala and Simpele, about 100 km from Lappeenranta to North-East. Korhonen does not mention Ahokas's age or year of birth, but she does say Ahokas was retired already by the time of her Degree Work (1981). Thus one could guestimate Ahokas had learnt this way of nalbinding perhaps in 1920's or 1930's.
So, once again one can say there is no one single, right way, of doing things :)