There may still be some old programs in some places, which can only run the old system.
But want to be able to execute and install some desired packages,
You may try this trick

Please note that if this system is important to you, please evaluate it yourself. It is recommended that you are in a Docker environment and have a backup image before trying it.

Open file

vi /etc/yum.repos.d/CentOS-Base.repo

Replace the three contents below

[base]
[updates]
[extras]

The content is as follows:

[base]
name=CentOS-$releasever-Base
# mirrorlist=http://mirrorlist.centos.org/?release=$releasever&arch=$basearch&repo=os&infra=$infra
# baseurl=http://mirror.centos.org/centos/$releasever/os/$basearch/
baseurl=https://vault.centos.org/6.10/os/$basearch/
gpgcheck=1
gpgkey=file:///etc/pki/rpm-gpg/RPM-GPG-KEY-CentOS-6

# released updates
[updates]
name=CentOS-$releasever-Updates
# mirrorlist=http://mirrorlist.centos.org/?release=$releasever&arch=$basearch&repo=updates&infra=$infra
# baseurl=http://mirror.centos.org/centos/$releasever/updates/$basearch/
baseurl=https://vault.centos.org/6.10/updates/$basearch/
gpgcheck=1
gpgkey=file:///etc/pki/rpm-gpg/RPM-GPG-KEY-CentOS-6

# additional packages that may be useful
[extras]
name=CentOS-$releasever-Extras
# mirrorlist=http://mirrorlist.centos.org/?release=$releasever&arch=$basearch&repo=extras&infra=$infra
# baseurl=http://mirror.centos.org/centos/$releasever/extras/$basearch/
baseurl=https://vault.centos.org/6.10/extras/$basearch/
gpgcheck=1
gpgkey=file:///etc/pki/rpm-gpg/RPM-GPG-KEY-CentOS-6

Clear

yum clean all

update

yum update