A, B, C, D, E and F are sitting around a circular table. Three of them face…

In a mixed-facing circular arrangement, first fix each person's seat using the clues, then apply a direction convention to read off left and right: a person facing the centre has their left hand toward the clockwise side and right hand toward the counter-clockwise side, while a person facing outward has the reverse - left is counter-clockwise and right is clockwise. Every seat must then be checked against all the clues at once, including the given totals for gender and facing direction.

1. On a 6-seat circle, moving 3 seats in either direction lands on the exact same (opposite) seat, so 'D sits third to the left of A' and 'A sits third to the right (clockwise) of the person immediately left of C' both place D directly opposite A - fix A at seat 1 and D at seat 4.

2. 'B is A's wife' and 'D is E's husband' mean B and A are opposite-gender spouses and D and E are opposite-gender spouses; since D is male, A is also male and B is female, while E is female - so the two female members are B and E, and A, C, D, F are the four male members.

3. The clue 'A sits third to the right (clockwise) of the one who is to the immediate left of C' is pure position arithmetic: the person 3 seats clockwise before A (seat 1) is seat 4, which is D. So D sits immediately to C's own left - a relation defined by C's facing, not D's.

4. Testing C facing outside: C's own left is the counter-clockwise seat, so setting that equal to D's seat (4) gives C at seat 5. C's own right is then the clockwise seat, seat 6, which by 'B is immediately right of C' must be B. The two remaining seats (2, 3) go to E and F; with 'F is immediately right of E' (E faces outside, so right = clockwise), E = 2 and F = 3. But then F's neighbours are seats 2 and 4 - E and D - putting F directly next to D, which breaks the clue that F is not the immediate neighbour of B or D. This branch is rejected.

5. So C faces the centre instead: C's own left is the clockwise seat, so setting that equal to D's seat (4) gives C at seat 3. C's own right is then the counter-clockwise seat, seat 2, which must be B. The two remaining seats (5, 6) go to E and F; with F immediately right of E, E = 5 and F = 6.

6. E and F face outside (given) and C faces the centre (from the accepted branch above). The two females (B and E) must face opposite directions: since E faces outside, B faces the centre, completing three centre-facing members (A, B, C). The stated 3-and-3 split then forces the remaining member, D, to face outside.

7. Every remaining clue checks out against this seating: A's neighbours (seats 2 and 6 = B and F) include the required female B; the two females B (seat 2) and E (seat 5) are not adjacent; and F's neighbours (seats 5 and 1 = E and A) do not include B or D.

Reading directly off the finished seat map, E (seat 5) is flanked by seat 4 and seat 6 - D and F - and both are male. So the two male immediate neighbours of E are D and F.