Answer
There are 8 valence electrons (an octet) surrounding $P$.
Work Step by Step
In the diagram, looking at the Lewis structure for $PF_3$ on the right side, we see that $P$ is surrounded by 3 lines and 2 dots.
That means there are 3 bonding pairs and 1 nonbonding pair of electrons surrounding $P$.
So, since each pair represents 2 valence electrons, there are 8 valence electrons (an octet) surrounding $P$.
