A problem in the Schubert Calculus
    There are 2 lines in space meeting four given lines (Here in blue, green, red, and black).
    Indeed, the blue, green, and red lines are members of one ruling of a unique hyperboloid of one sheet. Members of the other ruling are the lines meeting these three.
    The fourth black line meets the hyperboloid in two points, and through each of these points is a line meeting our four given lines.
   

The Theorem of Mukhin, Tarasov, and Varchenko is a way to choose the 4 lines to ensure that both solutions will be real.