For two lines two be skew to one another, they cannot be coplanar, they cannot intersect, and they cannot be parallel. With this in mind, we can rule out some lines.
Coplanar lines: All lines through F that are on plane FHE can be ruled out as EH lies on this plane.
Intersecting lines: The only line through F that intersects EH is EF. However, this line is a part of plane FHE so it is already ruled out.
Parallel Lines: The only line through F that is parallel to EH is EF. However, this line is a part of plane FHE so it is already ruled out.
Finally, we can draw DF, CF, BF, and AF which are all skew lines to EH that goes through F.
