After I create a calendar and I run request the status of the manager is NO Manager what do we have a tutorial about that or what could be the possible solution for that

Possibly concurrent manager service is down.
Login as System Administrator and navigate to Concurrent->Manager->Administer. See if Actual field displays 0 for "Internal Manager" then that confirms that concurrent manager is down.
Restart it from your operating system. adstrtal.sh script will start all services.

I did restart the script but it still not up

I check the Internal manager log file and found this error

Could not contact Service Manager FNDSM_ORAPROD_PROD. The TNS alias could not be located, the listener process on ORAPROD could not be contacted, or the listener failed to spawn the Service Manager process.

I don't know if I need to upgrade or apply a patch

Go to the directory:

/home/Oracle/PROD/inst/apps/PROD_linux/admin/scripts

Enter this command:

./adalnctl.sh status

See if your APPS listener is down. Start it using the command: adalnctl.sh start

I fix this Problem but not with restart the listener or the script ./adstrtal I did that several time but didn't work.

I installed oracle apps not on my personal computer on virtual machine but on another machine where I installed Linux Red hat, but I make some changes. I create a group "dba", 2 user oracle and applmgr and in the installation of oracle apps I assign oracle for database tier and applmgr for the inst tier with group dba and the problem was fix. I don't understand why this work and the single user didn't work but for now I continue the tutorials and the Concurent Manager is working

Good to know that the problem is resolved by the dual node installation.
It is a good idea to take a snapshot of your virtual machine so that you could rollback if something like this happen again.