In an arithmetic progression, consecutive terms differ by the same value.
So, we have
[tex]P-6 = 14-P[/tex]
which reflects the fact that the difference between P and 6 must be the same than the one between P and 14.
The equation solves to
[tex]2P=20\iff P=10[/tex]
And in fact, if you start with
[tex]6, 10, 14[/tex]
every pair of consecutive terms differ by 4.
