Given Information:
- The main memory has only 4 page frames.
- The page reference string is a b c d a e f b c d c e d b f.

Optimal Page Replacement Policy:
The optimal page replacement policy aims to minimize the number of page faults by replacing the page that will not be used for the longest period of time in the future.

Step-by-Step Explanation:

1. Initially, all 4 page frames are empty.
2. The first page reference is 'a'. As the page frame is empty, it will result in a page fault. The page 'a' is loaded into one of the empty page frames.
3. The second page reference is 'b'. Again, as the page frame is empty, it will result in a page fault. The page 'b' is loaded into the next empty page frame.
4. The third page reference is 'c'. Similar to the above steps, it will result in a page fault, and 'c' is loaded into the third empty page frame.
5. The fourth page reference is 'd'. Again, it will result in a page fault, and 'd' is loaded into the last empty page frame.
6. The fifth page reference is 'a'. Since 'a' is already present in one of the page frames, there is no page fault.
7. The sixth page reference is 'e'. As all the page frames are currently occupied, a page fault occurs. To determine which page to replace, we look ahead in the page reference string and find that 'b', 'c', and 'd' will be referenced in the future. We select the page that will be referenced last, which is 'b' in this case. So, the page frame containing 'b' is replaced with 'e'.
8. The seventh page reference is 'f'. As all the page frames are currently occupied, a page fault occurs. Similar to the previous step, we look ahead and find that 'c' and 'd' will be referenced in the future. We select the page that will be referenced last, which is 'c' in this case. So, the page frame containing 'c' is replaced with 'f'.
9. The eighth page reference is 'b'. Since 'b' is already present in one of the page frames, there is no page fault.
10. The ninth page reference is 'c'. Again, 'c' is already present in one of the page frames, so there is no page fault.
11. The tenth page reference is 'd'. Similar to the previous steps, there is no page fault as 'd' is already present in one of the page frames.
12. The eleventh page reference is 'c'. Again, 'c' is already present in one of the page frames, so there is no page fault.
13. The twelfth page reference is 'e'. As all the page frames are currently occupied, a page fault occurs. We look ahead and find that 'd' and 'b' will be referenced in the future. We select the page that will be referenced last, which is 'd' in this case. So, the page frame containing 'd' is replaced with 'e'.
14. The thirteenth page reference is 'd'. Similar to the previous steps, there is no page fault as 'd' is already