Translation:Those mutts usually live in that shack.
See the Tips and Notes for the "Affixes 2" skill: https://www.duolingo.com/skill/eo/Affixes-2
Briefly, it forms pejorative forms - words that mean the same thing but include a sort of "sneer" or "looking down your nose at".
For example, aŭto is a car and so aŭtaĉo might be something like "broken-down wreck"; ĉevalo is a horse and so ĉevalaĉo might be a "nag" - a word for a horse that's not particularly high quality.
In English, "live" can mean "to be alive," but it can also mean "to reside at," with the latter meaning behind used in the example sentence.
The word "stay" can mean to wait somewhere (ie, "please stay in the car while I run into the store") or to reside somewhere, but the latter meaning usually has a more short term nuance than does the word "live."
Example: If you asked a tourist where they were staying, they would give you the name of their hotel. If you asked that same person where they lived, they'd tell you their country/city/etc (the place where they reside long term).
Another example: If a friend from out of town called and asked if she could stay with me, I would assume she was visiting town for a few days and needed a place to stay. If she asked if she could live with me, I would assume she wanted to become roommates.
Since I'm assuming the mutts in the sentence reside in the shack long term, the better word for that sentence is "live."
"These" refers to something that is close to you, and "those" refers to something that is further away to you (possibly near the person you are speaking to, or possibly far from both speaker and listener).
In Esperanto, theoretically, the ti- correlatives refer to something far away, and to refer to something close, you have to add ĉi (tiuj ĉi "these ones", tie ĉi "here", tio ĉi "this", etc.). In general, Duolingo expects you to use these equivalencies.
In actual usage, plain ti- without ĉi may also refer to close things.