Minimum No of vertices will be 9.
Sum of degree of vetices = 2* edges
6*3 + K*v = 2*12 (Let there are rest v vertices each of degree K)
K*v = 24-18 = 6
K*v = 6
Now if degree of rest of the vertices is 2 then v = 3 and in total 9 vertices.
And if degree of rest of the vertices is 1 then v = 6 and in total 12 vertices.
Minimum vertices G can have 9.