Here is the reduction that SudokuSusser:
Squares R4C1, R5C1, R4C8 and R5C8 form a Type-4 Unique Rectangle on <56>. Because they share two rows, two columns, and two blocks, if they all had possibilities <56> then the puzzle would have two solutions; you could simply exchange the <5>s with the <6>s in the squares to get the other solution, and their common rows, columns and blocks would still contain one of each value. If you look carefully, you'll see that the only squares in block 6 that can contain <5> are the "roof" squares -- R4C8 and R5C8. Since one of these squares must be <5>, the only way to avoid the "deadly pattern" is if neither of them can contain <6>.
R4C8 - can remove <6> from <45678> leaving <4578>.
R5C8 - can remove <6> from <5678> leaving <578>.
If you are looking in a human point of vue, I really don't see why I can remove the 6 Candidate!
I agree that the candidate 5 must occupie one of the 2 square, but what is the logic behind the 6?
