I know to destroy a wall with a range combat attack, you must draw LOF to the square on the opposite side of the wall, and that square must be within your range.

However, what if your LOF can be drawn to the square on the opposite side of the wall, but your LOF goes along the direct diagonal, and does not go into the first square on the side of the wall of the attacking figure.

Can that character still destroy the wall?

nope. Your LoF must pass through the wall.

So if it was a corner wall like this

_| and you were on the direct diagonal of the wall you could not destroy either wall.

Agreeing with M.

I think people are using the word THE when they should be using the word A.
to destroy a wall, you must have range to A square on the other side of the wall the line of fire to which passes through the wall.

. . . . . . . .|. . . . . . . .
. . . . . . .t|. . . . . . . .
. . . . . . tx|. . . . . . . .
. . . . . . . . . . . . . . . .
. . . . . . . . . a. . . . . .
. . . . . . . . . . . . . . . .

the character A is on the exact diagonal to the corner of that wall, so the line of fire to the square X ("the" square on the other side of the wall) isn't any good. but a line of fire drawn to either of the squares marked T will pass through a wall, so as long as you have enough range, then destroying the walls is fine.

what you are forgetting you must target the square on the otherside. the only square is X.
So use it is THE not A.

A ranged combat attack can
be used to destroy a wall segment but only if a
single line of fire can be drawn to the center of
the square on the other side of the wall segment
that also crosses the square adjacent to the wall
segment.

When I asked this question, I was actually judging down at my venue, and the question came up.

I thought it is as you describe it, and that is the way I ruled it. But I got on the Realms and posted it here just to verify.

I had a question about destroying ways from NE, NW, SE, or SW directions, and I said no, you can't do that with a Close Combat Attack. I said to destroy a wall with a close combat attack, it had to be from the N, S, E, or W directions.

Your ruling was correct. Here is the relevant rules from the rulebook:
Notice how the rules for close and range are defined differently.

I gave rep to everyone that replied and helped out! Much thanks (Except for Maraud, because it would let me rep you again until I spread some more rep.)

Thanks I sure did. I pointed that out when I opened up the rulebook at the venue.

One player thought he could destroy a wall with a ranged combat attack as long as he could draw LOF to the center of the square on the opposite side of the wall that was to be destroyed. I said it had to travel through both squares on each side of the wall, and not just through the intersection of the wall to the opposite center of the square.

I told him if it went through the direct diagonal, "Wouldn't you be destroying to squares of wall then? Which wall do you choose? The one to right or to the left of the direct diagonal?" I said that is why it would work, because he had to target the actual wall, not the intersection going through the squares of the wall.

But thank you for your quick help, as it was during a tournament, and that put it to rest really quick.