ans C
i solved it in another way
Given |x| <1, let x= 1/2
3+6 x 2 + 9 x 4 +12 x 6... = 3(1+2 x 2 + 3 x 4+4x 6) =3(1+ 2*1/4+3*1/16+4*1/64) = 21/4 ~ 5
Check in each option....
a) if x=1/2 , 3/(1+x 2)=12/5 <5 Not the answer
b) if x=1/2 , 3/(1+x 2)2 = 48/25 <5 Not the answer
c) if x=1/2 , 3/(1-x 2)2=16/3 ~ 5 Hence the answer
d) if x=1/2 , 3/(1-x 2)=4 <5 Not the answer