Explanation:

Let’s break down the problem and evaluate each option:

- X works 1/6 of work per hour, Y does 1/8 per hour, Z does 1/8 per hour.

- Only one can work in an hour, and can't work two hours in a row.

- To finish fastest, alternate between X (fastest) and Y/Z.

- In 2 hours: X+Y or X+Z = (1/6)+(1/8) = 7/24 of the work.

- In 6 hours: 3 times (X+Y or X+Z) = 3×7/24 = 21/24, that is, 3/8 work remains.

- In the 7th hour: The fastest available is Y or Z (since X worked in 6th hour), so 1/8 more done.

- After 7 hours: 21/24 + 1/8 = 21/24 + 3/24 = 24/24 = 1, work complete.

Now, let’s see which option matches:

- 6 hours 15 minutes (6.25 hours)—Not enough (work in 6.25 hours with pattern is less than 1).

- 6 hours 30 minutes (6.5 hours)—Still a fraction short.

- 6 hours 45 minutes (6.75 hours)—Just short of total.

- 7 hours—This is right.

So, Option 4 (7 hours) is correct.

- Only way to alternate and use all workers, under given rules, is to take 7 hours.

- Sequence: X-Y-X-Z-X-Y-X or similar ensures minimum time.