In this case, "con" means "with" (the first option when hovering, at least now). Additionally, "lavoro" is the first person singular (I work) present tense conjugation of "lavorare" (to work), so the "work" is done by "me" not by the "certain people" (third person plural) in the sentence. If the "certain people" were working, you would use "lavorano". So the direct translation, keeping the same word order as the italian is: "With certain people I do not work", which is awkward in English, and we would reorder it to say: "I do not work with certain people"
'Persone' is the plural of 'persona' and is used when referring to specific people. If you say 'those people over there' you would use 'persone.' Gente is more general, meaning people in general or an unspecified number. Saying 'certa gente' implies you mean a group of people that share something in common, like race, gender, religion, etc. You can use 'gente' for groups or to mean everyone in the world / people in general.
My translation of "I won't work with certain people" seems very close to the Duolingo version of "I don't work with certain people". My translation was marked incorrect. It was fascinating to see many others having problems with this phrase. Agreed that "I will not work with certain people" is also a very good translation. They all capture the meaning. Having grown up with Italian spoken at home in Australia and having studied it at high school, albeit many years ago, I have a fairly good command of both languages. It seems at times that Duolingo hasn't got enough versions of equivalent phrases in its database. . Having said that Duolingo Italian is still a very good course and one that I often recommend to many friends and relatives. Avanti ragazzi e ragazze
I am a native English speaker and this is the phrase I used. Thinking about it, although I am using the future tense, I am using it in a continuous sense i.e. from the past, now and into the future. There are lots of cases in Italian where a past tense is used in the present sense e.g. imperfect subjunctive which Duolingo has shown me so I would report this if I were you but don't expect any immediate response both now and in the future