The correct answer is $\boxed{\text{B) 36 ohms}}$.
In a parallel circuit, the total resistance is less than the resistance of any of the individual branches. This is because the current can flow through multiple paths, so the overall resistance is lower.
To calculate the resistance of a parallel circuit, we use the following formula:
$$R_T = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots + \dfrac{1}{R_n}$$
where $R_T$ is the total resistance, $R_1$ is the resistance of the first branch, $R_2$ is the resistance of the second branch, and so on.
In this case, we are given that $R_T = 12 \Omega$ and $R_1 = 18 \Omega$. Substituting these values into the formula, we get:
$$R_T = \dfrac{1}{R_2} = \dfrac{1}{12 \Omega} – \dfrac{1}{18 \Omega} = 36 \Omega$$
Therefore, the resistance of the other branch is $\boxed{36 \Omega}$.
Option A is incorrect because it is the resistance of one of the branches, not the resistance of the other branch. Option C is incorrect because it is the sum of the resistances of the two branches, not the resistance of the other branch. Option D is incorrect because it is twice the resistance of the other branch.