Bidirectional X-Cycle

The cells C9, D9, E8, E6, B6 and C4 form a bidirectional cycle: there are exactly two ways of placing the value 9 in these cells, forming two different possible configurations. Some 9s appear in a row, column or box regardless of which configuration is correct. Because one of the two configurations must be correct, other occurrences of the value 9 can be removed from these rows, columns or boxs.

The cycle is an X-Cycle because only a single value is involved. X is a value, so it's a variable, if you think that way. Bidirectional X-Cycles are also known as Fishy Cycles or Bilocation cycles.

The two configurations of the bidirectional cycle are enforced by two complementary, circular chains of implications. The details of each chain are given below.

Cycle details, forward direction (View 1):
(1) If C4 contains the value 9 then C9 cannot contain the value 9 (the value can occur only once in the col)
(2) If C9 does not contain the value 9 then D9 must contain the value 9 (only remaining position in the row)
(3) If D9 contains the value 9 then E8 cannot contain the value 9 (the value can occur only once in the box)
(4) If E8 does not contain the value 9 then E6 must contain the value 9 (only remaining position in the column)
(5) If E6 contains the value 9 then B6 cannot contain the value 9 (the value can occur only once in the row)
(6) If B6 does not contain the value 9 then C4 must contain the value 9 (only remaining position in the box)

Cycle details, reverse direction (View 2):
(1) If C4 does not contain the value 9 then B6 must contain the value 9 (only remaining position in the box)
(2) If B6 contains the value 9 then E6 cannot contain the value 9 (the value can occur only once in the row)
(3) If E6 does not contain the value 9 then E8 must contain the value 9 (only remaining position in the column)
(4) If E8 contains the value 9 then D9 cannot contain the value 9 (the value can occur only once in the box)
(5) If D9 does not contain the value 9 then C9 must contain the value 9 (only remaining position in the row)
(6) If C9 contains the value 9 then C4 cannot contain the value 9 (the value can occur only once in the col)

NOTE: if all hinters are selected all Bidirectional X-Cycles should (AFAIK) be found BEFORE we call the Unary Chainer, So you should (AFAIK) never see an X-Cycle hint. If all hinters are selected AND you're seeing an X-Cycle, then one of the previous (simpler) hinters has missed a trick!