To determine how long it will take Mr. A and Mr. B to complete the work together, follow these steps:

1. Calculate the work rates of Mr. A and Mr. B:

- Mr. A's work rate is:
\[
\text{Rate of Mr. A} = \frac{1 \text{ work}}{6 \text{ hours}} = \frac{1}{6} \text{ work per hour}
\]

- Mr. B's work rate is:
\[
\text{Rate of Mr. B} = \frac{1 \text{ work}}{14 \text{ hours}} = \frac{1}{14} \text{ work per hour}
\]

2. Add their work rates to find their combined work rate:

\[
\text{Combined rate} = \frac{1}{6} + \frac{1}{14}
\]

To add these fractions, find a common denominator (which is 42):

\[
\frac{1}{6} = \frac{7}{42}
\]

\[
\frac{1}{14} = \frac{3}{42}
\]

\[
\text{Combined rate} = \frac{7}{42} + \frac{3}{42} = \frac{10}{42} = \frac{5}{21} \text{ work per hour}
\]

3. Determine the time required to complete the work together:

The reciprocal of the combined work rate gives the total time:

\[
\text{Time} = \frac{1}{\frac{5}{21}} = \frac{21}{5} = 4.2 \text{ hours}
\]

4. Convert 0.2 hours into minutes:

\[
0.2 \text{ hours} \times 60 \text{ minutes per hour} = 12 \text{ minutes}
\]

So, the total time is:

B. 4 hours and 12 minutes