**Hint 1**: Consider using a hash map to store the frequency of each number modulo 24. This will help in efficiently finding pairs that sum to a multiple of 24.

**Hint 2**: For each number in the array, compute its remainder when divided by 24. Then, for each remainder `r`, check if the complement `(24 - r) % 24` exists in the hash map. If it does, increment the count by the frequency of the complement.

**Hint 3**: To avoid double-counting pairs, iterate through the array and for each element, only check complements that come after it in the array. This ensures each pair is counted exactly once.