Positions (i) and (ii) show the same cube. Which of the cubes (a) to (d) can be another position of it?

From (i) and (ii), B touches A, C, D and F, so B is opposite E; with C placed by (i), A is opposite F and C is opposite D. That rules out (c) (A next to F) and (d) (D next to C). (a) and (b) both show C, A and E together, but only (b) has them going round in the same direction as on the real cube; (a) is its mirror image.