Get rid of centos 6 … I’m sure that that OS is so out of date, and will have no route to update to modern software, cut your losses and install an OS such as rocky or alma, if you fancy a change you could install a debian based OS the choice is yours, you will get nowhere with centos 6
Of course it is possible to restart it on the command line. It’s the same as any other service.
systemctl restart webmin (on systemd systems, or service webmin restart on non-systemd Linux systems…there are also stop and start scripts in the install directory of Webmin if you used the tarball installation…which you definitely should not do, on any system with a supported package manager).
Webmin should have been installed using an RPM from the Webmin yum repository. If you did that, you can install an older version with yum install webmin-<version> (use yum list webmin --showduplicates to see what versions are available).
We don’t try to break old distributions, but we don’t try to support them, either, and CentOS 6 has been unsupported by the CentOS project for about four years, and it has a Perl version that was old even when CentOS 6 was new. Our oldest explicitly supported Perl version is now 5.16.1. (This is probably not a Perl version problem, as I think only Virtualmin has code that definitely uses newer features, but we’re not going to try to support a 15 year old Perl version on an OS that the vendor stopped supporting four years ago.)
In short, if you think it’s safe to run old software, you probably need to run an old Webmin, too. Whatever the last version that worked for you. There haven’t been major security issues in Webmin in quite a long time, so it’s probably not a security risk…but CentOS 6 certainly has numerous major unpatched security issues, so…I guess you don’t care much about security.
What I’d recommend is you upgrade to a supported distributions. CentOS 7 reaches end of life in a few days, so that’s not a suitable replacement. CentOS 8 reached end of life last month (and stopped being an EL style OS long before that). For CentOS users, the best upgrade path is Rocky 9 or Alma 9 (I use Rocky on all my servers). RHEL 9 would also be a good option, though it may or may not be free to use, depending on a few factors.