If the LCM of a and 18 is 36 and the HCF of a and 18 is 2,

$\operatorname{LCM}(a, 18)=36$

$\operatorname{HCF}(a, 18)=2$

We know that the product of numbers is equal to the product of their HCF and LCM.

Therefore,

$18 a=2(36)$

$a=\frac{2(36)}{18}$

$a=4$

Hence the correct choice is (c).