"You start vacation on July fourth."
Translation:Empiezas las vacaciones el cuatro de julio.
Next time please include your whole answer when making a comment like this (preferably a copy-paste). It would be surprising for Duo to remove a previously accepted answer, so maybe there was some error you didn't notice, like typing cuarto instead of cuatro or something. Without seeing exactly what you submitted there's no way to know why it might have been rejected, if it was an issue on Duo's side or something else.
To be a little more precise, empezar needs an a when it's followed by another infinitive verb, but not when it's followed by a noun. So e.g. "I start working" = "empiezo a trabajar"; "I start my job" = "empiezo mi trabajo". "You start travelling" = "empiezas a viajar"; "you start vacation" = "empiezas las vacaciones".
Why can't some people accept that a foreign language has another grammar than their own language. I'm Dutch-speaking which grammar isn't the same as the English, nor the Spanish. You have to study grammar; on internet you can find a lot of information or buy a grammarbook. Read the tips of Duolingo, giving to each lesson.
When you can't tell if the English "you" is formal or informal, plural or singular, Duo usually accepts all the alternative variations in the Spanish translation. If you find one that Duo overlooked a transition option for a particular sentence, please report it.
It's also helpful to post your full answer in the comments if you believe it should have been accepted but it wasn't, so other users can help double check if you had some other mistake.
Correct Spanish would translate to "The fourth of July". I'm not sure where the on went, but probably not necessary because you could write the English "You start vacation the fourth of July".
Thinking as I was writing, I realized that "the "Fourth of July has special meaning for US residents. In Spanish "the" is used for all dates: Not "December 20" but "the 20th of December".
Next time if you copy-paste your answer into your comment (or add a screenshot - instructions can be found here (link)) we can try to help look for any issues. Sometimes your own typos can be really hard to spot (cuarto instead of cuatro is a very common one to miss!) but a second person looking at it will be able to point them out. Or at least we can confirm if your answer looks fine and maybe it was some issue on Duo's end.
There's a guide on how to upload a screenshot here in case you'd still like to try sharing it: https://forum.duolingo.com/comment/33394339/GUIDE-How-To-Upload-A-Screenshot
I always recommend copy-pasting your answer into your comment if you don't see any reason why it's wrong. Maybe someone else can spot something you missed (even if you did check many times), or at least we can assure you that it does look fine. But otherwise there isn't really any value in a comment like this, since we can't tell if it was a glitch, or a subtle typo, or what.