Each of the 9 letters can be dropped into any of the three letter boxes, and they can be distributed independently. Therefore, the total number of arrangements for each letter is 3 (three choices of boxes). Since there are 9 letters, we calculate the total number of combinations by raising of 3 (number of boxes) to the power of 9 (number of letters) for all possible combinations, i.e., 3^9. This results in the total of 19,683 ways in which the letters can be distributed in the boxes. Thus, option- 2 (19,683) is the correct answer.

Option- 1 (27) and option- 3 (729) both are the outcome of raising 3 to a smaller power, namely 3 and 6 respectively. These would be the number of ways if there were just 3 or 6 letters respectively. Option- 4 (19,680) is simply an incorrect calculation.