$T_{r+1}=nC_r1^{n-r}x^r$
$\Rightarrow 10C_r (1) ^{18-r}(x)^r$
The coefficient of $(2r+4)^{th}$ term in $(1+x)^{18}=18C_{2r+3}$
The coefficient of $(r-2)^{th}$ term $=18C_{r-3}$
Given :
Coefficient of $(2r+4)^{th}=(r-2)^{th}$ term
$2r+3=r-3$
$2r-r=-3-3$
$r=-6$
Or $2r+3+r-3=18$
$3r=18$
$r=6$
Hence (C) is the correct answer.