Start with simple cases;

No. of people 2 4 6 8

No of possibilities 1 2 5 14

Start with cases with need choices case:6 people

at 6, when its,

3 x 6

1 2 [ ] <- 2 possible answers

when its,

2 x 6

1 3 [ ] <- 2 possible answers ;; as 2/3 change placed its considered as +1 possibility

at 6 people (3+2)=5

at 8 people !refer people on the 1st row: (4+3+2)+(3+2)=14

at 10 people: (5 + 4 + 3 + 2) + (4 + 3 + 2) + (3 + 2) +(4 + 3 + 2) + (3 + 2) = 14 +9 +5 + 9 + 5 = 42

at 12 people FYI: (6 + 5 + 4 + 3 + 2) + (5 + 4 + 3 + 2) + (4 + 3 + 2) + ( 3 + 2) + (5 + 4 + 3 + 2) + (4 + 3 + 2) + ( 3 + 2) + (4 + 3 + 2) + ( 3 + 2) + (5 + 4 + 3 + 2) + (4 + 3 + 2) + ( 3 + 2) + (4 + 3 + 2) + ( 3 + 2) = 48 + 28 +14 + 28 + 14 = 132

If you would like to read how one primary school worked on the problem then find an article in the Mathematics Teaching number 188 (published by the Association of Teachers of Mathematics).