To determine the maximum number of edges of a regular octahedron that can be seen from a point outside the octahedron, we start by considering the geometric properties of the octahedron and the visibility conditions.

A regular octahedron has 12 edges. The visibility of an edge from an external point depends on whether the plane formed by the point and the edge intersects the octahedron only along that edge.

Consider a regular octahedron with vertices at $A_1(0,0,1), A_2(0,0,-1), B_1(0,1,0), B_2(0,-1,0), C_1(1,0,0),$ and $C_2(-1,0,0)$. Let $P(x_0, y_0, z_0)$ be a point outside the octahedron such that $x_0, y_0, z_0$ are nonnegative real numbers with $x_0 + y_0 + z_0 > 1$.

The octahedron is bounded by the inequality $|x| + |y| + |z| \leq 1$.

To determine the visibility of edges, we analyze the conditions under which the plane formed by $P$ and an edge intersects the octahedron. If $x_0 + y_0 \leq 1 + z_0$, the plane $PA_2$ intersects the octahedron, making edges $A_2B_1, A_2B_2, A_2C_1,$ and $A_2C_2$ not visible. Similarly, if $y_0 + z_0 \leq 1 + x_0$ or $z_0 + x_0 \leq 1 + y_0$, we cannot see certain edges.

However, for $P$ in the region defined by $x_0 + y_0 > 1 + z_0$, $y_0 + z_0 > 1 + x_0$, and $z_0 + x_0 > 1 + y_0$, we can see the following edges:
- $A_1B_1, B_1C_1, C_1A_1$
- $A_1B_2, A_1C_2, B_1A_2, B_1C_2, C_1A_2, C_1B_2$

Thus, we can see a total of 9 edges from such a point $P$.

Therefore, the maximum number of edges of a regular octahedron that can be seen from a point outside the octahedron is:
$$\boxed{9}$$