@GuilhermePinto15 said in Permission:
In another words an email or file that says that i can use retropie to the project named"PAP - ArcadeDeck"
RetroPie - the setup scripts - is released under the GNU Public License (GPL), as mentioned in https://retropie.org.uk/about/legal/. You'll not get an email or file as you desire, but you can point your teacher to the Legal page and mention the GPL, which is a permissive usage license.
Note that this doesn't cover any games that you may have installed, which have their own license and usage terms.