The question is about placing 8 identical balls in two horizontal rows, one with 6 balls and the other with 2 balls.

Option 1 suggests 38 ways to do this. This seems to be the correct answer. By a basic permutation rule "n choose r", which is used to find the number of ways to choose r objects from a set of n objects without considering the order, there can be 8 choose 6 (since six balls are placed in one row) ways and that equals to 28 ways and 8 choose 2 (since two balls are placed in another row) ways and that equals to 28 ways too. Adding them up, we get a total of 56 ways, which contradicts with option 1.

Option 2 suggests 28 ways, which is the number of ways just considered for each row individually rather than the combined placements.

Option 3 suggests 16 ways, and option 4 suggests 14 ways. These two, however, don`t appear to align with the known combinations and numerical logic.

Alert - correct answer should be 56. In the given information, there seems to be a miscalculation or misunderstanding in calculating combinations. The correct number of ways should be 56 (28