Commentaire sur Parah 7:9

והורה הוראה – to permit or to forbid, to defile or to purify, to make exempt or to make liable.

One was carrying his water on his shoulder and he ruled in a matter of law, or showed others the way, or killed a snake or a scorpion, or picked up food in order to store it, it [the water] is invalid; But [if he picked up] food to eat, it is valid. [And if he killed] a snake or a scorpion that hindered him, it remains valid.
Rabbi Judah said: this is the general rule: If the act was is in the nature of work, the mixture is invalid whether the man stopped or not, If it was not in the nature of work: If he stopped, it is invalid;
But if he did not stop it remains valid.
Section one: In all of these cases, the action is considered work and it invalidates the water that he is carrying from being used for the red cow ritual. However, the mishnah goes on to list circumstances in which said action doesn't invalidate the water.
When it comes to picking up food, it depends what his purpose is. If he picked it up to store it away, it counts as work and the water is invalid. However, if he picked it up in order to eat it, it doesn't count as work. Eating, in other words, is not work.
If he killed the snake or scorpion because it was hindering his progress, the water remains valid. Actions he needs to do in order to simply progress on his way do not invalidate the water.
Section two: Rabbi Judah sets up a general principle that relates to these types of situation, and show that issuing a ruling or giving someone directions also do not always disqualify the water. If an action was done in the nature of work, meaning it is something that is generally considered to be work, then it doesn't matter whether he stopped on the path or not, it disqualifies the water he is carrying. In other words, the mere action itself is disqualifying.
However, if it is not a matter of work, such as issuing a ruling or showing someone the way, then it depends on whether he stopped or not. If he stopped, then this stoppage to perform another action can invalidate the water. But if he did not stop, then the water remains valid.

ודבר שאינו משום הלכה – as for example, a lesson and showing [others] the way.

אם עמד – if he was delayed there because of this.

פסול – because of distraction. And this is the Halakha.