To determine the time it takes for Mr. A and Mr. B to complete the work together, we can use the concept of work rates.

- Mr. A's work rate: \( \frac{1}{6} \) of the work per hour.
- Mr. B's work rate: \( \frac{1}{14} \) of the work per hour.

Together, their combined work rate is:
\[
\frac{1}{6} + \frac{1}{14}
\]

To add these fractions, find the common denominator:
\[
\frac{1}{6} = \frac{7}{42}, \quad \frac{1}{14} = \frac{3}{42}
\]
\[
\text{Combined rate} = \frac{7}{42} + \frac{3}{42} = \frac{10}{42} = \frac{5}{21}
\]

Thus, working together, they complete \( \frac{5}{21} \) of the work in one hour.

To find the total time to complete the work:
\[
\text{Time} = \frac{1}{\frac{5}{21}} = \frac{21}{5} \text{ hours} = 4.2 \text{ hours}
\]

Convert 0.2 hours to minutes:
\[
0.2 \times 60 = 12 \text{ minutes}
\]

Therefore, it will take them 4 hours and 12 minutes to complete the work together.

So the correct answer is B. 4 hours and 12 minutes.