12. There is a class of students going boating. They calculated that if they added one more boat, there would be exactly 6 people per boat; if they reduced one boat, there would be exactly 9 people per boat. Question: How many students are there in the class?
36 people
12.【Solution】First, add one more boat, then each boat will have exactly 6 people. Then remove two boats, there will be $6 \times 2=12$ students left. Change to 9 people per boat, which means each boat increases by 9 $-6=3$ people, which can exactly accommodate the remaining 12 students, so there are now $12 \div 3=4$ boats, and the total number of students in the class is $9 \times 4=36$ people.

【Another Solution】From the conditions of the problem, the total number of students in the class is a multiple of both 6 and 9, and thus a common multiple of 6 and 9. The least common multiple of 6 and 9 is 18. If the total number is 18, then 6 people per boat would require $18 \div 6=3$ boats, and 9 people per boat would require $18 \div 9=2$ boats, meaning 6 people per boat would require one more boat than 9 people per boat. However, according to the conditions of the problem, 6 people per boat requires 2 more boats than 9 people per boat. Therefore, the total number of people should be $18 \times 2=36$.

Answer: This class has a total of 36 people.