Parallel tangency for immersions into Euclidean spaces

Let M and N be two smoothly immersed manifolds of codimension 2 in the Euclidean space R2n. We study the enumerative problem: find the number of the pairs (x,y)∈M×N of points so that Mx is parallel to Ny, where Mx⊂R2n is the tangent space to M at x.