Identifying the pattern:
To find the next number in the sequence, we need to first identify the pattern in the given numbers: 66, 120, 180, 124.

Step 1: Analyzing the differences between consecutive numbers:
Let's calculate the differences between consecutive numbers to see if there is a consistent pattern:
- The difference between 120 and 66 is 54.
- The difference between 180 and 120 is 60.
- The difference between 124 and 180 is -56.

Step 2: Identifying the pattern:
From the differences calculated, we can observe that:
- The difference between the first two numbers (54) is equal to the difference between the second two numbers (60).
- However, the difference between the second and third numbers (-56) is not consistent with the previous differences.

Step 3: Considering multiplication:
Since the differences in the sequence are not consistent, let's consider multiplication as well. We can see that:
- 66 multiplied by 2 is equal to 132, which is close to the second number (120).
- 120 multiplied by 1.5 is equal to 180, which is the third number.

Step 4: Combining addition and multiplication:
Based on the analysis above, it seems that the pattern in the sequence involves both addition and multiplication. Let's express the pattern using these operations:
- Start with the first number (66).
- Multiply it by 2 to get the second number (132).
- Add 12 to the second number to get the third number (144).
- Multiply the third number by 1.25 to get the fourth number (180).
- Subtract 56 from the fourth number to get the fifth number.

Step 5: Calculating the next number:
To calculate the next number in the sequence, we follow the pattern identified above:
- Start with the fourth number (180).
- Multiply it by 1.25 to get the fifth number (225).
- Subtract 56 from the fifth number to get the next number.

Final answer:
Based on the pattern, the next number in the sequence after 124 is 225. Therefore, the correct answer is not among the options provided.