The average height of the students of a class would be increased by 6 cm if 12 children were 8 cm taller. How many children are there in the class?

Let's solve this problem step by step:

1. Let's assume that there are "x" children in the class.
2. The average height of the students would be increased by 6 cm if 12 children were 8 cm taller.
3. This means that the total increase in height would be 6 cm * x (the number of children).
4. Additionally, the 12 children who are 8 cm taller would contribute to this increase in height.
5. So, the total increase in height would be 6 cm * x + 12 children * 8 cm.
6. According to the problem, this increase in height is equal to the average height of the students.
7. Therefore, we can set up the equation: 6 cm * x + 12 children * 8 cm = x * average height.
8. Simplifying the equation, we get: 6x + 96 = x * average height.
9. We know that the average height is the total height divided by the number of children, so we can rewrite the equation as: 6x + 96 = x * (total height / x).
10. Simplifying further, we get: 6x + 96 = total height.
11. Now, we need to find the total height of all the children in the class.
12. To do this, we can multiply the average height by the number of children: total height = average height * x.
13. Substituting this into the equation, we get: 6x + 96 = average height * x.
14. Rearranging the equation, we have: 6x = average height * x - 96.
15. Factoring out the x on the right side, we get: 6x = x * (average height - 96).
16. Dividing both sides by (average height - 96), we get: 6x / (average height - 96) = x.
17. Finally, we can solve for x by dividing both sides by x: 6 / (average height - 96) = 1.
18. Therefore, the number of children in the class is 6 / (average height - 96).

Please note that we need to know the average height of the students in order to find the number of children in the class.