First, we solve the quadratic equation for set $A$: $x^2 - 5x + 6 = 0 \implies (x-2)(x-3) = 0$, so $A = \{2, 3\}$. For set $B$, $x^2 = 9 \implies x = \pm 3$, so $B = \{-3, 3\}$. The symmetric difference $A \Delta B$ is defined as $(A \cup B) - (A \cap B)$. Here $A \cup B = \{2, 3, -3\}$ and $A \cap B = \{3\}$. Thus, $A \Delta B = \{2, -3\}$. The number of elements in $A \Delta B$ is $n = 2$. The number of elements in the power set $P(S)$ is given by $2^n$. Therefore, $n(P(A \Delta B)) = 2^2 = 4$. Option 1 is incorrect because it is the cardinality of the symmetric difference itself, not its power set. Options 3 and 4 are incorrect because they use wrong values for $n$ in the $2^n$ formula.