Solution: $0,2,4$
If the three lines form a triangle, then there are 4 circles, namely the incircle and the three excircles. If the three lines concur or are all parallel, then there are 0 circles. If two lines are parallel and the third is not, then there are 2 circles lying between the two parallel lines, one on each side of the transverse line. These are the only possible configurations, so the answers are 0,2 , and 4 .
7. Three distinct lines are drawn in the plane. Suppose there exist exactly $n$ circles in the plane tangent to all three lines. Find all possible values of $n$.