Don't go with a way that's not true, this is going to cost alot of time so you can keep track of the index of the original string, so the function will look like:

void backtrack(int x, int y, int i) { ... }

And when you want to go to for example (x+1, y+1) you should check this:

if (x+1 < n && y+1 < n && mat[x+1][y+1]  == final[i])

     backtrack(x+1, y+1, i+1); 

And the same for the 3 remaining calls.

Base case: (i == final.size())