To solve this problem, we need to understand the relationship between the number of workers and the time taken to complete a task, which is an example of inverse proportion.

Here's the step-by-step explanation:

1. First, identify that if the number of workers increases, the time taken to complete the same task decreases proportionally. This is because more workers can complete more work in the same amount of time.
2. We know from the problem statement that 4 workers can complete the task in 8 days. Let's denote this as \(W = 4\) (workers) and \(D = 8\) (days).
3. The total amount of work can be expressed as \(W \times D = 4 \times 8 = 32\) worker-days (where the product of the number of workers and the number of days represents the total work).
4. We need to find out how many days \(D'\) it will take 8 workers (\(W' = 8\)) to complete the same task:
5. Since the amount of work is constant, we have:
6. \(W \times D = W' \times D'\)
7. Substitute the known values:
8. \(4 \times 8 = 8 \times D'\)
9. Solving for \(D'\) gives:
10. \(D' = \frac{4 \times 8}{8} = 4\).
11. Therefore, 8 workers will take 4 days to complete the same task.

The correct answer is 4 days, which matches the option provided.