A turing machine is defined as a 7-tuple $M = \langle Q, \Gamma, b, \Sigma, \delta, q_0, F \rangle$. The set $F$ in the tuple is the set of final states or accepting states. So any other states other than the ones in $F$ are the rejecting states. You can consider the language that $M$ covers as $L$. So $L'$ will be the language (set of phrases) that $M$ never accepts. If you create another Turing machine $M'$ for $L'$, then the set of final states for $M'$ in combination with $F$ is the answer you are looking for.
But determining whether or not your Turing machine ever reaches these states is another question overall. It is generally impossible to know whether or not a Turing machine will halt beforehand. So if you could count the number of ways that a Turing machine will halt (not could halt), you are basically raising a serious contradiction with the halting problem.