Okay, here are the steps to solve this problem:
1) 24 is divisible by 3. So any sum of 3 multiples of 3 that adds to 24 will have at least one multiple that is 6 (2 x 3) or 9 (3 x 3).
2) We can represent the multiples as: 3n, 3n+1, 3n+2 where n is an integer.
3) The 3n terms can only be 3, 6, 9, 12, 15, 18, 21. The 3n+1 terms can be 4, 7, 10, 13, 16, 19, 22. And 3n+2 terms can be 5, 8, 11, 14, 17, 20, 23.
4) We need to count the number of combinations of these terms that add to 24. Some options are:
3 + 9 + 12 = 24
6 + 9 + 9 = 24
12 + 6 + 6 = 24
15 + 3 + 6 = 24
18 + 3 + 3 = 24
5) In total, there are 5 options with 3 terms.
6) Additionally, we could have 4 term sums like:
3 + 6 + 9 + 6 = 24
6 + 6 + 6 + 6 = 24
There are 2 four-term options.
7) In total, there are 5 + 2 = 7 number of ways to write 24 as a sum of at least 3 positive integer multiples of 3.
Does this help explain the steps? Let me know if you have any other questions!