About primitive roots.

Question

Assuming $6$ is a primitive root mod $p$ ( for some odd prime $p$) ( assuming this is possible) then could $p$ have another distinct primitive root $n$ (such that $1 \lt n \lt (p-1)$) where $(6,n) = 1$?

Answer 1

Modulo 17, there are 8 primitive roots, including 6, 10, 12, 14.