ahaselhu is correct; the solution given does not indicate whether coin 12 is heavy or light. The third and fourth paragraphs should be changed to read:

There are two possibilities. Either they balance, or they don’t. If they balance, then the different marble is in the group 9,10,11,12. So for our second weighing we would put 9,10,11 in the left pan and 1,2,3 on the right. If they balance, weigh 12 against any other marble to find out if it’s lighter or heavier. If they don’t balance, you know that the odd marble is either (a) lighter than the others if 9,10,11 weighs less than 1,2,3 or (b) heavier than others id 9,10,11 is heavier than 1,2,3. Now you just need to use your last weigh to find the odd marble. Weigh 9 against 10. If they balance, 11 is the odd marble, and you already know if it’s heavier or lighter. If they don’t balance and (a) was true, then the lighter of 9 and 10 is the odd marble. If (b) was true, then then heavier of 9 and 10 is the odd one.