You can directly upgrade/migrate your 6.0 VC to latest version of 6.7.
You need to have the latest backup of your vcenter and DB servers.
you may check the upgrade path using this link , this link contains upgrade path for all VMware products . I always refer this link before planning for upgrades.
1. Direct upgrade is possible from vCenter Server version 6.0 to 6.7
2. Use third-party backup solution for more safety to keep entire of VCSA VM (I want to say do not confine to vCenter itself backup by its management portal 5480)
I put my YouTube channel video link here. It's about upgrade procedure from VCSA6.0 to 6.7, I hope this can be helpful for you.Please mark my comment as the Correct Answer if this solution resolved your problem
- As already stated, the direct update is possible (see attached diagram).
- vCenter Server 6.7 U3 daes not exist. The latest build released si 6.7 U2c of July 16 2019 (see attached diagram).
- Before proceeding you must disable the DRS
- Backup of the VCSA before starting.