This is a solution
33 on the hard interview questions node
The problem basically asks you to create four equilateral triangles of the same size with six toothpicks. A bit of analysis will tell us that four triangles require twelve toothpicks, and since we only have six to work with, that means each toothpick must appear in two triangles. So every triangle has to border three other triangles (one on each side).
Think outside of the plane. It's a tetrahedron (a three-sided pyramid).