The function given is $P(x) = x(x - 6)(x + 8)$.

Finding the y-intercept:

The y-intercept is found by substituting $x = 0$ into the function.

$P(0) = 0(0 - 6)(0 + 8) = 0 \cdot (-6) \cdot 8 = 0$

Thus, the y-intercept is $0$.

x-intercepts:

As already shown, the x-intercepts are $x = 6$ and $x = -8$, which are obtained by setting $P(x) = 0$ and solving each factor:

$x = 0, \, x - 6 = 0 \, \Rightarrow x = 6, \, x + 8 = 0 \, \Rightarrow x = -8$

So, the function has the x-intercepts $0, 6, -8$.

Would you like further details or clarifications?

Here are 5 related questions you could explore:

1. How can we find the vertex of the quadratic function?
2. What does the graph of this function look like?
3. How do we factor more complex polynomials?
4. What are the applications of x- and y-intercepts in real-life problems?
5. Can this function have more than 3 intercepts in any situation?

Tip: When finding intercepts, always set the opposite variable to zero: for x-intercepts set $y = 0$ and for y-intercepts set $x = 0$.