The answer is six. Each line can intersect with each other line. If we call the lines A, B, C and D, imagine the intersections. Line A can intersect B, C and D - that's three. B can intersect A, C and D, but we have already counted where A and B intersect, so we just get another two. Then C can intersect A, B and D, but we have counted A-C and B-C already so we just get one more, where C and D intersect. So the answer is 3+2+1=6.