To solve this problem, we can use the concept of combinations.

Given:
Number of gentlemen (G) = 8
Number of ladies (L) = 4
Total members in the committee (N) = 6

We need to find the number of ways to form a committee of 6 members such that it contains at least 3 ladies.

Case 1: 3 ladies and 3 gentlemen
In this case, we need to select 3 ladies from the available 4 ladies and 3 gentlemen from the available 8 gentlemen.
The number of ways to select 3 ladies out of 4 is denoted by C(4, 3) = 4C3 = 4.
Similarly, the number of ways to select 3 gentlemen out of 8 is denoted by C(8, 3) = 8C3 = 56.

Therefore, the total number of ways to form the committee with 3 ladies and 3 gentlemen is 4 * 56 = 224.

Case 2: 4 ladies and 2 gentlemen
In this case, we need to select all 4 ladies from the available 4 ladies and select 2 gentlemen from the remaining 8 gentlemen.
The number of ways to select 2 gentlemen out of 8 is denoted by C(8, 2) = 8C2 = 28.

Therefore, the total number of ways to form the committee with 4 ladies and 2 gentlemen is 1 * 28 = 28.

Case 3: 5 ladies and 1 gentleman
In this case, we need to select all 4 ladies from the available 4 ladies and select 1 gentleman from the remaining 8 gentlemen.
The number of ways to select 1 gentleman out of 8 is denoted by C(8, 1) = 8C1 = 8.

Therefore, the total number of ways to form the committee with 5 ladies and 1 gentleman is 1 * 8 = 8.

Case 4: 6 ladies and 0 gentlemen
In this case, we need to select all 4 ladies from the available 4 ladies.
The number of ways to select 4 ladies out of 4 is denoted by C(4, 4) = 4C4 = 1.

Therefore, the total number of ways to form the committee with 6 ladies and 0 gentlemen is 1.

Now, we can find the total number of ways by summing up the number of ways from each case:

Total number of ways = 224 + 28 + 8 + 1 = 261.

Therefore, the correct answer is option A: 252.