Whether "six months" means six calendar months or 180 days is a fascinating question, but ultimately not an important one in this situation.
Even if your mother did technically overstay for 4 days in her last visit, such a short overstay does not attract a re-entry ban (when leaving voluntarily, on her own expense after less than 90 days overstay, and with no other aggravating circumstances). So whether she will be allowed in again will depend on whether she can convince the immigration officer that she is a "genuine visitor" at that time. This is exactly the same standard as if she haven't overstayed!
Sure enough, the IO will be able to see the overstay (if an overstay it is) when making this determination -- but her travel history is available to them anyway. And the crucial information they will get out of that, no matter whether it's technically an overstay or not, is that she stayed for half a year and left right on the date when she reasonably believed she was required to. That is evidence of, on one hand, willingness to comply with the rules (which is a good thing), but on the other hand also of a desire to stretch her visit as long as possible (which could be cause for concern).
On yet another hand, the fact that she stayed out for more than a year after that long visit makes it less likely that she'll be seen as trying to live in the UK through long successive visits (which would be a really bad thing). So it could go either way -- but my unfounded wild guess would be that she'd probably be allowed in after some questioning.
At the end, in either case, it comes down to whether the IO finds her and her plans credible or not.
