To determine the largest initial value of semaphore S for which at least one P(S) operation will remain blocked, we need to consider the number of P(S) and V(S) operations issued and their order of execution. Let's analyze the given information step by step:

Given:
- Number of P(S) operations issued = 20
- Number of V(S) operations issued = 12

To find the largest initial value of S, let's assume S = X and analyze the possible scenarios.

1. X = 0:
- In this case, all 20 P(S) operations will be blocked as the semaphore value is initially 0.
- Since no V(S) operation is executed yet, there is no chance for any P(S) operation to be unblocked.
- Therefore, the largest initial value of S for which at least one P(S) operation will remain blocked is not possible when X = 0.

2. X = 1:
- In this case, the first P(S) operation will block as the semaphore value becomes 0.
- After that, all subsequent P(S) operations will also block as the semaphore value remains 0.
- Since no V(S) operation is executed yet, there is no chance for any P(S) operation to be unblocked.
- Therefore, the largest initial value of S for which at least one P(S) operation will remain blocked is not possible when X = 1.

3. X = 2:
- The first P(S) operation will decrement S from 2 to 1, so it will not block.
- The second P(S) operation will decrement S from 1 to 0, so it will block.
- Since no V(S) operation is executed yet, there is no chance for the second P(S) operation to be unblocked.
- Therefore, the largest initial value of S for which at least one P(S) operation will remain blocked is not possible when X = 2.

4. X = 3:
- The first P(S) operation will decrement S from 3 to 2, so it will not block.
- The second P(S) operation will decrement S from 2 to 1, so it will not block.
- The third P(S) operation will decrement S from 1 to 0, so it will block.
- Since no V(S) operation is executed yet, there is no chance for the third P(S) operation to be unblocked.
- Therefore, the largest initial value of S for which at least one P(S) operation will remain blocked is not possible when X = 3.

5. X = 4:
- The first P(S) operation will decrement S from 4 to 3, so it will not block.
- The second P(S) operation will decrement S from 3 to 2, so it will not block.
- The third P(S) operation will decrement S from 2 to 1, so it will not block.
- The fourth P(S) operation will decrement S from 1 to 0, so it will block.
- Since no V(S) operation is executed yet, there is no chance for the fourth P(S) operation to be unblocked.
- Therefore, the largest initial value of S for which at least one P(S) operation will remain blocked is not possible when X = 4.

6. X = 5:
- The first P