**Probability of getting an odd number on a die roll of 6:**

We have to find the probability of getting an odd number of $6$. To find the probability of getting an odd number of $6$ when rolling a fair six-sided die, we can break it down into the possible outcomes:

1. Rolling a $1$ (odd) - Probability = $\frac{1}{6}$
2. Rolling a $2$ (even) - Probability = $\frac{1}{6}$
3. Rolling a $3$ (odd) - Probability = $\frac{1}{6}$
4. Rolling a $4$ (even) - Probability = $\frac{1}{6}$
5. Rolling a $5$ (odd) - Probability = $\frac{1}{6}$
6. Rolling a $6$ (even) - Probability = $\frac{1}{6}$.

The probability of getting an odd number on a die roll is $\frac{1}{2}$, since there are three odd numbers $(1, 3,$ and $5)$ and three even numbers $(2, 4,$ and $6)$ on a standard six-sided die. To find the probability of getting an odd number of $6$, we have to add the probabilities of these three outcomes:

$\text{Probability of getting an odd number of 6 = (Probability of rolling a 1) + (Probability of rolling a 3) + (Probability of rolling a 5)}$
$\text{Probability of getting an odd number of 6} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$

So, the answer is B. $\frac{1}{2}$.