The set {x>0 , y>0} is the first quadrant.
{3x + 2y > 18} is the domain above the red line.
{6x + 7y < 42} is the domain below the green line.
So, the intersection is this obtuse tiangle in the first quadrant adjacent to the x-axis.
I do not see much sense in the question of the problem.
You can estimate the range of this linear function z = 3x + 3y by evaluating its values in the vertices of the triangle.
(Then is it typical problem of the linear programming).
May be other tutors have some ideas?
