Let's extend the line that passes through points E and F, EF.
From the figure, we can see that EF is a horizontal line along one of the sides of the cube. Any line parallel to this line must also be horizontal and cannot intersect with it. We can find these lines along the remaining edges of the cube.
There are three parallel lines: AB, DC, and HG. However only HG contains G, so that is our answer.
