Here the rule which is applicable on the series: 6 9 12 15 is Rule D: Divide by 2 and add 3 as:
Start with the number 6.
62=3,3+3=6
Now, take the number 12.
122=6,6+3=9
Take the number 18.
182=9,9+3=12
Finally move on to the number 24.
242=12,12+3=15
Hence, Rule (D) is the correct answer.