Question Analysis:
The question asks for the median of the series of all the even terms from 4 to 296. The series includes all the even numbers between 4 and 296. We need to find the middle value of this series, which is the median.

Step-by-Step Solution:
To find the median of the series, we need to follow these steps:

Step 1: List all the even terms from 4 to 296:
The even terms between 4 and 296 are: 4, 6, 8, 10, 12, ..., 296.

Step 2: Calculate the total number of terms in the series:
To find the median, we need to know the total number of terms in the series. In this case, we have a sequence of even numbers, so the total number of terms can be calculated using the formula:
Number of terms = (Last Term - First Term) / Common Difference + 1.

In this case, the first term is 4, the last term is 296, and the common difference is 2 (since we are dealing with even numbers). So, the number of terms = (296 - 4) / 2 + 1 = 146.

Step 3: Find the middle term:
Since we have an odd number of terms (146), the median will be the middle term. To find the middle term, we divide the total number of terms by 2 and round up to the nearest whole number. In this case, the middle term is the 73rd term.

Step 4: Find the value of the middle term:
To find the value of the middle term, we can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference.

In this case, the first term is 4, the common difference is 2, and the value of n is 73. So, the value of the middle term is 4 + (73 - 1) * 2 = 4 + 144 = 148.

Step 5: Determine the median:
The median is the middle value of the series, which is 148.

Conclusion:
The median of the series of all the even terms from 4 to 296 is 148. Therefore, the correct answer is option C) 150.