I think the letters are irrelevant, unless one is going to restrict the space to those paths which form, say, words found in the AHD or OED or what have you.
Otherwise, it's a distraction.

It seems obvious that 9 is the number - say 4 for the base of the loop, 4 to loop around and 1 to pass through. The knot starts in the drawing plane. The ampersand is the "hole" through which the "string" must loop to form the knot.

1
*---*
\
\ 2
\
* & *
\ /
4 \ / 3
\ /
*


Dotted line 5 comes out of the plane to a point in front of point A.
Dotted line 6 returns to the plane.

1 A 6
*---*...*
. \
5. \ 2
. \
* *
\ /
4 \ / 3
\ /
*

The segment from B to a point BEHIND & is number 7.

1 A 6
*---*...* B
. \.
5. .\ 2
. \
* & *
\ /
4 \ / 3
\ /
*


Eight is from the point behind & to & itself.
Nine is from & to any point in the plane in front
of the drawing plane.

Intuitively, one has to have a loop with a hole in it.
The catch here is whether points 3 and 4 really need to
be in the plane. Seems like with suitable refinements,
the space of possible solutions is not that great -
perhaps one could have a computer check into it.

k