Explanation:
Let's solve this problem step by step:

1. Define the Work Rates:
- Let the number of days A takes to complete the work alone be \( A \) days.
- Let the number of days B takes to complete the work alone be \( B \) days.
- According to the problem, A is twice as good a workman as B, so A's work rate is twice that of B.

2. Express Work Rates:
- The work rate of A is \( \frac{1}{A} \) of the work per day.
- The work rate of B is \( \frac{1}{B} \) of the work per day.
- Since A is twice as efficient as B, \( \frac{1}{A} = 2 \times \frac{1}{B} \), which means \( A = \frac{B}{2} \).

3. Combined Work Rate:
- Together, A and B can complete the work in 14 days, so their combined work rate is \( \frac{1}{14} \) of the work per day.
- The combined work rate of A and B is \( \frac{1}{A} + \frac{1}{B} \).

4. Substitute and Solve:
- Substitute \( A = \frac{B}{2} \) into the combined work rate equation:
\[
\frac{1}{A} + \frac{1}{B} = \frac{1}{\frac{B}{2}} + \frac{1}{B} = \frac{2}{B} + \frac{1}{B} = \frac{3}{B}
\]
- Since their combined work rate is \( \frac{1}{14} \):
\[
\frac{3}{B} = \frac{1}{14}
\]
- Solving for \( B \):
\[
B = 3 \times 14 = 42 \text{ days}
\]
- Therefore, A's time to complete the work alone is:
\[
A = \frac{B}{2} = \frac{42}{2} = 21 \text{ days}
\]


A alone can complete the work in 21 days.

The correct answer is C. 21 days.