Suppose that 7 machines can complete a certain task in 12 days. If there are 6 machines, how many days would it take for them to finish the same task?

Step 1 ：Let's denote the number of machines as \(m\), the number of days as \(d\), and the total work as \(W\). We know that \(W = m \times d\).

Step 2 ：Given that 7 machines can complete a task in 12 days, we can write this as \(W = 7 \times 12\).

Step 3 ：We want to find out how many days it would take for 6 machines to complete the same task, so we set up the equation \(6 \times d = 7 \times 12\).

Step 4 ：Solving for \(d\), we get \(d = \frac{7 \times 12}{6} = 14\).

Step 5 ：Final Answer: It would take 6 machines \(\boxed{14}\) days to complete the task.