To solve the equation \(6Pn = 360\), we need to understand that \(6Pn\) represents the number of permutations of 6 objects taken \(n\) at a time.

The formula for permutations is given by:

\[
6Pn = \frac{6!}{(6-n)!}
\]

We are given that \(6Pn = 360\), so:

\[
\frac{6!}{(6-n)!} = 360
\]

Let's calculate \(6!\) (which is the factorial of 6):

\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
\]

Now, we can set up the equation:

\[
\frac{720}{(6-n)!} = 360
\]

Next, solve for \((6-n)!\):

\[
(6-n)! = \frac{720}{360} = 2
\]

Now, we need to find which factorial equals 2:

\[
1! = 1, \quad 2! = 2
\]

This means \( (6-n)! = 2 \) implies \( 6-n = 2 \).

So:

\[
6 - n = 2
\]

Now, solve for \( n \):

\[
n = 6 - 2 = 4
\]

### Final Answer:
The value of \( n \) is 4.

Would you like to see more details or have any other questions? Here are some related questions you might find interesting:

1. What would the equation look like if \(5Pn = 120\)?
2. How do you calculate permutations for larger values of \(n\)?
3. How are permutations different from combinations?
4. Can you use permutations in probability calculations?
5. What if the permutation was \(7Pn = 2520\)? How would you solve it?

**Tip:** When solving permutation problems, breaking down the factorials into smaller components can make it easier to find the solution.

Learn how to solve the permutations problem 6Pn = 360 with a detailed step-by-step solution. This problem involves understanding permutations, factorial calculations, and solving equations. Suitable for high school students.

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