...from your other thread, I gathered this information:
So my understanding is that your old bike is a Diamondback something, that still works, but you want something newer. And you use it mainly for transportation, presumably in a small town or urban environment.
Wheels size, in and of itself, is just something around which a bicycle frame is designed. But it is true, as has been repeated here, that mostly you see 24" wheels on bicycles for younger riders, who are physically smaller than adults, mostly. If you are a smaller person, a 24" wheeled bike might fit you fine, but it will be a chore to find one that is of better quality, overall, especially if you are looking at Walmart or on Amazon.
I gave you that link to the current Diamondback website. Diamondback used to be something you saw more at dedicated bike shops, for sale. I don't know how they market their bikes now.
People could probably give you better information if you stated your specific needs (urban transportation and grocery shopping ?). Also some idea of whether you are a very small, or larger person might indicate that a 24" wheel size could work for you. I still worry about the whole rack attachment requirement. You might be better off going with a different brand of bicycle, and looking at something marketed specifically as an urban all purpose bicycle. Some of those come with the rack already installed.
I'm not sure that going from 26" wheels to 24" wheels will make it appreciably easier to get your bike in and out of your building.
Many lower priced bicycles use a nutted rear wheel, rather than a quick release wheel, because it's cheaper to source them. Quality varies.
REI has some good deals on this sort of bicycle, and sometimes they go on sale. But I don't think you'll find one with 24" wheels there.