Answer
See the answer below.
Work Step by Step
Rules for quantum numbers:
1. $0\leq\ell\leq n-1$
2. $-\ell\leq m_\ell\leq \ell$
3. $m_s=\pm 1/2$
By definition: $4p\rightarrow n=4, \ell=1$
Valid $(n,\ell,m_\ell, m_s)$ sets:
(4,1,-1,-1/2),(4,1,-1,+1/2), (4,1,0,-1/2),(4,1,0,+1/2), (4,1,+1,-1/2),(4,1,+1,+1/2)
