Numbers which are co-prime to $18:= 1,5,7,11,13,17$ there are 6 such numbers.

$(or)$ $18=3^2*2^1$, then numbers co-prime to $18:(3^2 - 3^1)*(2^1-2^0) = 6*1=6$

Now we can eliminate the options! $(C)$ is the correct one.

PS:This problem is same as to find the number of generators in a cyclic group of order n.