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