Pattern Analysis:
To find the next number in the given series, it is important to identify the pattern or rule that governs the sequence. Let's analyze the given series step by step:

Step 1:
Looking at the first few numbers, we can observe that the series starts with 3 and then increases by 1. The first number is followed by an increment of 1, resulting in the second number 4.

Step 2:
Continuing with the pattern established in step 1, the series now increases by 3. The second number 4 is followed by an increment of 3, resulting in the third number 7.

Step 3:
In the next step, the series again increases by 1. The third number 7 is followed by an increment of 1, resulting in the fourth number 8.

Step 4:
Continuing with the pattern established in step 3, the series now increases by 3. The fourth number 8 is followed by an increment of 3, resulting in the fifth number 11.

Step 5:
Following the same pattern, the series again increases by 1. The fifth number 11 is followed by an increment of 1, resulting in the sixth number 12.

Step 6:
Based on the pattern observed in the previous steps, we can conclude that the series alternates between an increment of 1 and an increment of 3.

Next Number:
To find the next number in the series, we need to continue the established pattern. Since the previous increment was 1, the next increment should be 3.

Therefore, the next number in the series would be obtained by adding 3 to the last number, which is 12.

Calculation:
12 + 3 = 15

Conclusion:
Hence, the number that should come next in the given series is 15. Therefore, the correct option is D) 15.