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First of all..it is one-sixth.
ratio of surface are of moon/earth=4* \pi * radius of moon^{2}  /4* \pi * radius of earth^{2} ............in question radius of earth would be given.so just input the values.

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Let diameter of moon=d
⇒radius of moon=d/2=r
⇒diameter of earth=D
since, d is 1/4 D
⇒D=4d=diameter of earth
radius of earth,R=D/2=4d/2
⇒R=4×2r÷2 = 4r
ratio of surface areas=surfacearea of moon : surfacearea of earth
   =4πr² : 4πR²
   =r² : (4r)²
   =r² : 16r²
⇒ ratio1:16
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