Solution:

$N=m_{1} N_{1}$

$m_{1}=2 \quad N_{1}=3$

$x(k)=\sum_{n=0}^{N_{1}-1} x\left(n m_{1}\right) \ W_N^{nm_1k \ N_1 - 1} + \sum^{N_1 - 1}_{n = 0} \ x(nm_1 + 1)^{(nm_1 + 1) k}_{W_N}$

$+\cdots+\sum^{N_1 - 1}_{n = 0} \ x(nm_1 + (m_1 - 1))^{nm_1 + (m_1 - 1)) \ k }_{W_N}$

$x(k)=\sum_{n=0}^{2} x(2 n) w_{6}^{2nk}+\sum_{n=0}^{2} x(2 n+1)w^{(2n + 1)}_{6}$

$x(k)=\sum_{n=0}^{2} x(2 n) w_{3}^{n k}+\sum_{n=0}^{2} x(2 n+1) w_{3}^{nk} \cdot w_{6}^k$

$X(R)=\underbrace{\sum_{n=0}^{2} x(2 n) w_{3}^{nk}}_{x_{1}(R)} + \sum w_{6}^{k} \underbrace{\sum_{n=0}^{2} x(2 n+1) w_{3}^{nk}}_{x_{2}(R)}$

$x(k)=x_{1}(k)+w_{6}^{R} x_{2}(R) \quad$ - - - - [1]

$x_{1}(k)=\sum_{n=0}^{2} x(2 n) w_{3}^{nk}=x(0)+x(2) w_{3}^{R}+x(4) w_{3}^{R}$ - - - - [2]

$x_{2}(k)=\sum_{n=0}^{2} x(2 n+1) w_{3}^{nk}=x(3)+$$x(3) w_{3}^{k}+x(5) \frac{2 k}{3}$ - - - [3]