What starting value to use for Newton method? I have a function:

$x^3-$$6x^2$$+8$

for which I need to find the root(s).
The Newton Method states that I must have a number $x_n$ to have as a starting value before evaluating, I have seen many people use $x_n$=$1$ as their starting number, and even $-1$, how do I know which one to use? especially for functions with multiple zeroes.

Generally speaking, given a function for which you want to find a root using Newton's method, you have to have some prior knowledge of the rough location of a zero, and the behavior of the function near that zero, in order to pick a good starting value of Newton's method (for example as in the answer of @ClaudeLeibovici).
If you don't have such prior knowledge, finding a choice of the starting value which "works" is a difficult and, sometimes, indeterminate problem. You can see this quite clearly in the paper of Curry, Garnett and Sullivan entitled "On the iteration of a rational function: computer experiments with Newton's method", in which they study the behavior of (complex valued) Newton's method for polynomials of the form $z^3 + (A-1) z - A$.
