Introduction:
In this problem, we are given a sequence of numbers and we need to find the missing numbers. The given sequence is as follows:
11, 7, 49, _, 13, 8, 54, _, 15, 4, ?, ?

Observations:
To find the missing numbers, let's analyze the given sequence and identify any patterns or relationships between the numbers.

1. First set of numbers: 11, 7, 49
2. Second set of numbers: 13, 8, 54
3. Third set of numbers: 15, 4, ?

Pattern in the first set of numbers:
Let's examine the first set of numbers: 11, 7, 49

- The second number (7) is the square root of the first number (11).
- The third number (49) is the square of the second number (7).

Therefore, it seems that each number in the first set is related to the previous number through squaring or finding square roots.

Pattern in the second set of numbers:
Now let's analyze the second set of numbers: 13, 8, 54

- The second number (8) is obtained by subtracting 5 from the first number (13).
- The third number (54) is obtained by multiplying the second number (8) by 6.

Hence, it appears that each number in the second set is related to the previous number through subtraction and multiplication.

Pattern in the third set of numbers:
Finally, we need to find the missing numbers in the third set: 15, 4, ?

To identify the pattern, let's examine the relationship between the first two numbers in the third set.

- The second number (4) is obtained by subtracting 11 from the first number (15).

Calculating the missing numbers:
Following the observed patterns, we can calculate the missing numbers:

1. First missing number:
- The square root of 49 is 7.
- Therefore, the first missing number should be the square of 7, which is 49.

2. Second missing number:
- Subtracting 5 from 13 gives us 8.
- Thus, the second missing number should be 8 multiplied by 6, which is 48.

3. Third missing number:
- Subtracting 11 from 15 gives us 4.
- Therefore, the third missing number should be 4 squared, which is 16.

4. Fourth missing number:
- As the second missing number is 48 and the third missing number is 16, we can find the difference between them: 48 - 16 = 32.
- Hence, the fourth missing number should be 16 added to 32, resulting in 48.

Final sequence:
By calculating the missing numbers, the final sequence becomes:
11, 7, 49, 48, 13, 8, 54, 48, 15, 4, 16, 48.

Conclusion:
By analyzing the given sequence and identifying the patterns, we were able to find the missing numbers as 49, 48, 16, and 48.