@jrusitahabla - In English we don't say "the work" when talking about it as a location, which is how it is used in this exercise.
"The work" as a process/a thing is fine, though. If the sentence were "Мама уже начала работу", then "Mom already started the work" would sound OK (as long as we knew what work was being talked about).
When you use the preposition "na" to describ the physical location of somebody or something, it puts the noun in prepositional case. The -a ending becomes -e in such case. Words that end in -ie and -iya take the -ii ending (Stantsiya -> na stantsii). If it's a masculine word ending in a consonant then you add a -e to the end of it (kompyuter - v kompyutere)
When the preposition "na" is used to describe the destination of an action (going to a place, setting something down on something), then it'll be accusative, and the -a in rabota becomes an -u (rabotu).
I am sorry for the translit, do not have the RU keyboard set up on my phone.