The question is about arranging 6 identical balls in 3 rows of a square that is divided into 9 smaller squares. Each row must contain at least one ball.

Option 1 - 27: This would be the number of ways if there are 3 balls and each ball is to be placed in a different row. But here we have 6 balls, so this option is incorrect.

Option 2 - 36: This would be the number of ways if there are 4 balls and each row should get at least one. However, we have 6 balls, so this option is incorrect.

Option 3 - 54: This would be correct if 6 balls were to be arranged across 9 squares without the condition that each row should get at least one ball. But here, each row must contain at least one ball, making this option incorrect.

Option 4 - 81: This is the correct answer. Since every row needs to have at least one ball, we can think of it as placing 3 balls in 3 rows, or 3^3 ways = 27 ways. Then for the remaining 3 balls, they can be placed in any of 9 squares, or 3^3 ways = 27 ways.