Sue de Coq lives in the overlap between a line and a box — those three shared cells. When two of them jointly hold candidates that split cleanly into a set completed within the line and a set completed within the box, both digit sets get locked simultaneously. The line loses its set outside the overlap, and the box loses its set outside the overlap, in one move.
The overlap cells r4c1 and r4c2 (blue) split {2,5,8} between row and box — eliminating the 2 in the row and the 8 in the box (red).
Take the overlap of row 4 with its left box: r4c1 holds 2-5 and r4c2 holds 5-8, a combined set of {2, 5, 8} in two cells. The 2 can only be completed out in the row, the 8 only in the box, and the 5 is consumed inside the overlap either way. Both directions get swept at once: the 2 at r4c7 leaves the row, the 8 at r5c2 leaves the box.
The candidate split must be airtight — every digit assignable to exactly one side (row, box, or locked in the overlap). If a digit could complete on either side, the pattern proves nothing and the 'eliminations' are guesses.