Here we'll talk about the basic laws of Yayin Nesech (libation wine) that gets mixed with kosher wine. Yayin Nesech is prohibited to benefit from, as we've been learning. It also prohibits a mixture even in the smallest amount. If a tiny bit of Yayin Nesech is mixed with a larger amount of kosher wine, all of that wine becomes prohibited. That halacha (Jewish law) is not only for wine. It's also for any other type of liquid, libation, or offering that was brought as an offering to an idol.
But that's only talking about min bemino. If you have a mixture of something with its own kind, yayin be-yayin (wine in wine), u'mayim be-mayim (water in water), bechol shehu (any amount). When Yayin Nesech gets mixed with kosher wine, or Nesech water (libation water) gets mixed with permitted water, that prohibits the mixture even in the smallest amount. But yayin be-mayim (wine in water) and u'mayim be-yayin (water in wine) are be-noten ta'am. But Yayin Nesech mixed with permitted water, or Nesech water mixed with permitted wine, only prohibits the mixture if there's be-noten ta'am, when it gives enough flavor to the mixture. That means you could taste it. You could taste whatever was prohibited in that liquid. You could taste that it's actually there.
If you're talking about kosher good wine that had mayim that came from an offering mixed in with it, if you could tell that the wine has been really, really watered down, that's enough to be called noten ta'am, and therefore that mixture would be prohibited. But less than that, the mixture would not be prohibited. If you have water—a regular bottle of water that had no issue with it whatsoever—and a little bit of wine was added to it, and you could tell that there was wine, that it's not just simply a bottle of water but there's wine added to it, that's enough to detect, and you could taste it. That would mean it's a problem because it's noten ta'am. But if you can't even detect the taste of that wine, it would be no issue whatsoever.
And that's the general rule. If you have a prohibited food or drink of one kind that becomes mixed in with a permitted food of the same kind, then even the smallest amount is a problem, like forbidden wine that gets mixed with permitted wine. Even the smallest amount is an issue. But when you're talking about a permitted substance being mixed with something that is not its own kind, let's say you have water and wine, like we had in the last part of the Mishnah, then that mixture becomes prohibited only when the forbidden item gives or enhances the flavor.