Again, it needs no trial and error at all, once you realise what the actual problem is.
Have you heard of the 15 puzzle? This is exactly the same, except just a smaller size. You have 8 different symbols and a blank square that you start in - you have to end up with each of the symbols in their correct square (doors are the symbols / surrounded by red is what doors should be where).
All you have to do each move is slide one of the symbols next to the blank square into the blank square - by walking between the squares.
So if you label the 8 different symbols from 1 to 8 in some particular order:
123
. 45
678
Then you want to end up with
Click here to view the secret text
×
516
482
37 .
.
An example first move would be to slide the 4 to the left.