First of all, you can choose to deploy OVA against of OVF. However, change your browser and test you can select all of the related files for OVF format or not ...
Anyway, because you export the VM/VA from a higher version of ESXi, you cannot import it to an older version like 6.0, probably you choose the higher version of hardware compatibility for the VM when you create it. In one case if you set up hardware version compatible with ESXi 6.0 when you work in the 6.7 environment, then you can add it to the ESXi 6.0 with any possible method (OVA, Backup&Recovery & so on)Please mark my comment as the Correct Answer if this solution resolved your problem
When exporting a template from a browser, it can only be OVF, and OVA cannot be selected.
I know that you can use the 6.0 web client to import, but if you can only select one file when importing from the vi client, the hardware version of the virtual machine is 8 so 6.0 version is compatible. I'm just trying to import it from the vi client. Any way to export OVA file from browser, thank you for your answer
Here's your options if I am getting it right.
1. Your VM in source 6.7 vCenter should have hardware version below 11 to make this migration work since ESXi in vCenter 6.0 will support hardware version 11 VMs only.
2. Try OVFtool.
3. If your destination VC is 6.0 U3, try VMware fling: Cross vCenter Workload Migration Utility | VMware Flings
4. Use vCenter Converter if your VM hardware version is above 11.
5. Make a cold clone of VM in source 6.7 vCenter then downgrade VM hardware version to 11 before exporting. You can find guide online for same.