As of Craft 2.7.0, Craft 2 can run on PHP 7.2.
You're probably trying to install Craft 2 using PHP 7.2 (which doesn't have mycrypt installed by default), which isn't supported (see here: https://docs.craftcms.com/v2/requirements.html).
Your options are to:
Use Craft 3, which supports PHP 7.2 and doesn't use mcrypt.
Install mcrypt on PHP 7.2, but ...
Brad Bell mentions this about Craft:
Being a self-hosted PHP web application is a hard life. Your parents try to raise you correctly and equip you with the tools necessary to successfully go out into the world and live on some stranger's unknown, unfriendly and oftentimes hostile server environment so you can serve up web pages, but things are stacked ...
If you follow the instructions here: Local Development with Vagrant / Homestead and can't get it working, let me know.
That's the exact procedure I use whenever I set it up; I just did it 3 weeks ago to set up a new machine running Homestead without incident.
I don't know what version of RHEL they're running, but it could certainly be added. Whether your IT department will support it or if that breaks some support contract your company has with RH is another question all-together.
FWIW, Craft 3/Yii 2 has done away with mcrypt in favor of OpenSSL, so it's not an issue there.