The number of the second type of circular permutations required is
$$
\begin{aligned}
M(2,2,2) & =\frac{1}{2} \cdot T(2,2,2)+\frac{1}{2} \cdot \frac{\left(\frac{6}{2}\right)!}{\left(\frac{2}{2}\right)!\left(\frac{2}{2}\right)!\left(\frac{2}{2}\right)!} \\
& =\frac{1}{2} \times 16+\frac{1}{2} \times 6=11 .
\end{aligned}
$$

Typically, the counting problem of the first type of circular permutations is referred to as the counting problem of bracelet styles; the counting problem of the second type of circular permutations is referred to as the counting problem of necklace styles. For example, from Example 7.13, there are 16 different styles of bracelets that can be made using 2 red beads, 2 blue beads, and 2 yellow beads; from Example 7.14, there are 11 different styles of necklaces that can be made using 2 red beads, 2 blue beads, and 2 yellow beads.
Example 7.14 Find the number of second-kind circular permutations made from 2 $a$s, 2 $b$s, 2 $c$s.