With 12 phalanges on each hand that can be marked by the thumb of the same hand, there are 12 possibilities on each hand, or 12 * 12 = 144 possible combinations of marked phalanges with two hands.
The article made it clear, both through the text and the picture, that only one hand used the phalanx counting method, while the other hand simply used digits as we do today. Thus, with 12 phalanges to choose from on one hand and 5 digits to choose from on the other, we have 12 * 5 = 60 combinations.
The very image and text used in the article implies that the original poster is correct.
Look at the example for 32 - it is given as 8 + 2x12. The hand on the right has two fingers extended. Clearly all fingers can be extended in this image, and then the number would be 8 + 5x12 = 68. If the left hand is used to count to 12, the number is 12 + 5x12, or 12+60=72.
Either the limit is 60, or the images/text in the article are wrong.
You're right! I didn't look closely enough. You can indeed symbolize 72 with the method shown in the picture.
Now that I finally get what viggity was saying however, I think that what you can count to with two hands wasn't what was significant -- it was that a full, open hand was worth 60.
12 from hand one + 12 * 5 from hand two = 72