Translation:Kati is painting workers and engineers.
If it were, it would not suggest that engineers are not workers, as this sentence wrongly does.
The translation of munkás as "worker" might be a bit unlucky. I think "labourer" might be closer. A munkás is usually one who does mainly physical work, like a construction worker.
Kati munkásoknak és mérnököknek fest.
The -nak/-nek suffix is pretty equivalent to the dative case in other European languages, what you express in English with "to" or "for" someone or something.
Vowel harmony. If your base word has e, é, ö, ő, ü, ű as its vowels, it prefers having those same vowels in the suffixes, too. The same counts for words with a, á, o, ó, u, ú.
I translated munkásokat as laborers and though it was accepted -- it was flagged as a typo, it should have been labourers. I don't see how to report translation things like this (not one of the 3 options given).