There are 26 letters and you draw 2 at random so the first letter is one of 26 and the second one of 25 so there are 26*25 = 650 ways to pick two letters.

The letter A is adjacent to B and H so that is 2 ways to pick adjacent letters with A as the first letter.

B is next to 4 letters so there are 4 ways to pick adjacent letters with B as the first, and AB is different to BA.

If you go through the wall you get the following ways per brick

2 4 4 4 4 4 2

5 6 6 6 6 5

3 6 6 6 6 6 3

3 4 4 4 4 3

and that sums to 116 so you get 116/650 which simplifies to 58/325