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?