Explanation:

The optimal replacement policy is a theoretical algorithm that always selects the page that will not be used for the longest period of time in the future. However, it is practically impossible to implement this algorithm in real systems as it requires knowledge of future page references.

The given page reference string is: 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6.

We have 3 page frames initially empty, so the first 3 page references will result in page faults as there are no pages in the frames. The frames will be filled as follows:

1. Page fault: 1 is not in the frames. Page 1 is loaded into the first frame.
2. Page fault: 2 is not in the frames. Page 2 is loaded into the second frame.
3. Page fault: 3 is not in the frames. Page 3 is loaded into the third frame.

Now, the frames contain pages 1, 2, and 3. The next page reference is 4. As there is no page fault, the frames still contain pages 1, 2, and 3.

The next page reference is 2. As page 2 is already in the frames, there is no page fault.

The next page reference is 1. As page 1 is already in the frames, there is no page fault.

The next page reference is 5. As page 5 is not in the frames, a page fault occurs. The optimal replacement policy would replace page 3 with page 5 as it will not be used for the longest period of time.

The next page reference is 3. As page 3 is already in the frames, there is no page fault.

The next page reference is 2. As page 2 is already in the frames, there is no page fault.

The next page reference is 4. As page 4 is not in the frames, a page fault occurs. The optimal replacement policy would replace page 1 with page 4 as it will not be used for the longest period of time.

The next page reference is 6. As page 6 is not in the frames, a page fault occurs. The optimal replacement policy would replace page 2 with page 6 as it will not be used for the longest period of time.

Therefore, the total number of page faults using the optimal replacement policy is 7.