To solve $4P2$ when $p = 6$, we need to use the formula for permutations:

$nP_r = \frac{n!}{(n - r)!}$

In this case, $n = 6$ and $r = 2$. So,

$6P2 = \frac{6!}{(6 - 2)!} = \frac{6!}{4!}$

Now, calculate the factorials:

$6! = 6 \times 5 \times 4! \quad \text{(since 4! will cancel out with the denominator)}$

So,

$6P2 = \frac{6 \times 5 \times 4!}{4!} = 6 \times 5 = 30$

Thus, $6P2 = 30$.

Would you like further details on permutations or other questions? Here are a few more to explore:

1. How do permutations differ from combinations?
2. What is the general formula for combinations?
3. How do you calculate $5P3$?
4. What are some real-life examples of using permutations?
5. What happens if the number of selections (r) is equal to n?

Tip: Remember that in permutations, the order of selection matters!