H.M. = 4 ⇒ (\dfrac{2xy}{x+y}=4\Rightarrow xy=2(x+y))

(2A+G^2=27), (A=\dfrac{x+y}{2}), (G^2=xy)

[ 2\cdot\dfrac{x+y}{2}+xy=27\implies x+y+xy=27 ]

From H.M.: (xy=2(x+y)). Let (s=x+y), (p=xy=2s)

[ s+2s=27\implies 3s=27\implies s=9,\ p=18 ]

Numbers: 3 and 6.

Answer: 3 and 6