2019 AMC 12B Problem 11

Two edges determine a plane exactly when they are coplanar, that is, parallel or intersecting. The $12$ edges split into $3$ directions of $4$ parallel edges, giving $3\binom{4}{2}=18$ parallel pairs. Edges sharing a vertex give $8\binom{3}{2}=24$ intersecting pairs. The total is $18+24=42.$ Thus, D is the correct answer.