Example 3  Choose 1 young man and 1 young woman from each of the four groups to perform a circle dance, with the rule that men and women must alternate, and two people from the same group cannot be adjacent. How many different team formation variations are there?
Let $A, B, C, D$ represent the four young women selected by the four groups, and $a, b, c, d$ represent the four young men selected by the four groups, where $A_{a}, B_{b}, C_{i}, D_{d}$ are from the same group. The number of ways to arrange the young women is $(4-1)!=3$! methods. In Figure 2-1, the numbers (1)(2)(3)(4) are the positions of the young men, arranged in ascending order as $d, c, b, a$ and $c, b, a, d$ in two ways, with other arrangements not meeting the requirements. Therefore, the total number of different formations is $2 \cdot 3!=12$ kinds.