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.