8-6. In a kindergarten, 150 children are standing in a circle. Each child is looking at the teacher standing in the center of the circle. Some children are wearing blue jackets, and the rest are wearing red ones. There are 12 children in blue jackets whose left neighbor is in a red jacket. How many children have a left neighbor wearing a jacket of the same color?
Answer: 126.

Solution I. Let each of the children say whether the color of their jacket is the same as that of the child to their left. We need to find out how many children will say "The same."

Let's find out how many children said "Different." Note that if we go around the circle, the jacket colors of such children alternate. Indeed, if someone has a red jacket and their left neighbor has a blue one, then further on, there are several (possibly one) children in blue jackets until someone says that their left neighbor has a red jacket. Similarly, if someone has a blue jacket and their left neighbor has a red one. Therefore, among the children who said "Different," there are an equal number of children in red and blue jackets. According to the problem, there are 12 children in red jackets. Thus, the total number of children who said "Different" is twice as many, i.e., 24. Therefore, the answer is $150 - 2 \cdot 12 = 126$.

Solution II. We know that 12 children in blue jackets have a neighbor to their left dressed in a red jacket. This means that in the circle, there are 12 pairs of adjacent children, where the right one is in a red jacket and the left one is in a blue jacket. We will denote such pairs as BK. What do we need to find? We need to find the number of pairs of adjacent children whose jackets are of the same color, i.e., pairs RR and BB.

The main observation for this solution is as follows: the total number of pairs BK and BB equals simply the number of children in blue jackets, since each of them has some neighbor to their right. If this neighbor is in a red jacket, we count them in pairs BK, and if they are in a blue jacket, we count them in pairs BB. So, let the total number of children in blue jackets be $s$. There are 12 pairs BK, so there are $s - 12$ pairs BB.

Similarly, the total number of pairs BK and RR equals the number of children in red jackets. The number of children in red jackets is $150 - s$, and there are 12 pairs BK, so there are $138 - s$ pairs RR. Therefore, the total number of pairs BB and RR is $(s - 12) + (138 - s) = 126$.