We use a double loop to inspect all the pairs.

When determining if any of the pair satisfies the condition, it is a good idea to maintain a variable that stores whether the conditions so far are all satisfied, just as we did in ABC277-B Editorial. This way, the implementation is simplified. See also the sample code.

Sample code (Python):

n, m = map(int, input().split())
s = [input() for i in range(n)]
res = 0
for i in range(n):
    for j in range(i + 1, n):
        ok = True
        for k in range(m):
            if s[i][k] == 'x' and s[j][k] == 'x':
                ok = False
        if ok:
            res += 1
print(res)