Parallel tangency for immersions into Euclidean spaces

Let M and N be two smoothly immersed manifolds of codimension 2 in the Euclidean space R 2 n . We study the enumerative problem: find the number of the pairs ( x , y ) ∈ M × N of points so that M x is parallel to N y , where M x ⊂ R 2 n is the tangent space to M at x.