Explanation:

To find out how many days Y can finish the work alone, we can use the following logic:

- Let the time X takes to finish the work alone be $x$ days.

- Y takes five days more than X, so Y takes $x+5$ days alone.

- The work done by X in one day is $\frac{1}{x}$.

- The work done by Y in one day is $\frac{1}{x+5}$.

- Together, they finish the work in 6 days, so their combined one day work is $\frac{1}{6}$.

Set the equation for combined work and solve:

$$\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}$$

Solving this equation gives $x=10$ (time X takes alone). Thus, Y takes:

$$x+5=10+5=15$$

days to complete the work alone.

- Option 1: 16 - Too high.

- Option 2: 12 - Too low.

- Option 3: 15 - Correct.

- Option 4: 10 - It's the time X takes alone, not Y.

Correct answer: Option 3: 15