Answer
The number of different $m_i$ 's is $2(3)+1=7$.
Since $L_{\mathrm{orb}, z} \propto m_{\ell}$, there are a total of seven different values of $L_{\mathrm{orb}, z}$.
Work Step by Step
The number of different $m_i$ 's is $2(3)+1=7$.
Since $L_{\mathrm{orb}, z} \propto m_{\ell}$, there are a total of seven different values of $L_{\mathrm{orb}, z}$.