Concept:For two numbers a and b, arithmetic mean (AM) = 2a+b​ and geometric mean (GM) = ab​.Explanation:Given AM = 6.50, so 2a+b​=6.5 ⇒ a+b=13.Given GM = 6, so ab​=6 ⇒ ab=36.The numbers are the roots of x2−(a+b)x+ab=0, i.e., x2−13x+36=0.Factorising: (x−4)(x−9)=0, so x=4 or x=9.Thus the two numbers are 4 and 9.Answer:Option B: 9 and 4.