To determine the maximum value of n for the system to be deadlock free, we need to consider the number of available tape drives and the number of processes competing for them.

Given:
- There are six tape drives available.
- Each process may need two drives.

To avoid deadlock, we need to ensure that there are always enough tape drives available for each process to complete its task. This means that no process should be left waiting indefinitely for the required number of tape drives.

Let's consider different scenarios based on the number of processes:

1. n = 1:
- In this case, only one process is competing for the tape drives.
- As each process needs two drives, it will create a deadlock because there are not enough drives available.
- Therefore, n = 1 is not a valid option.

2. n = 2:
- With two processes competing for the tape drives, each needing two drives, the total number of drives required is 4 (2 * 2 = 4).
- Since there are six drives available, this scenario is deadlock free.
- Therefore, n = 2 is a valid option.

3. n = 3:
- With three processes competing for the tape drives, each needing two drives, the total number of drives required is 6 (3 * 2 = 6).
- In this scenario, all the available drives are required, leaving no drives for any additional processes.
- Therefore, n = 3 is not a valid option.

4. n = 4:
- With four processes competing for the tape drives, each needing two drives, the total number of drives required is 8 (4 * 2 = 8).
- Since there are only six drives available, this scenario will create a deadlock because there are not enough drives for all the processes.
- Therefore, n = 4 is not a valid option.

5. n = 5:
- With five processes competing for the tape drives, each needing two drives, the total number of drives required is 10 (5 * 2 = 10).
- Since there are only six drives available, this scenario will create a deadlock because there are not enough drives for all the processes.
- Therefore, n = 5 is not a valid option.

Based on the analysis above, the maximum value of n for the system to be deadlock free is n = 2, making option B the correct answer.