There is a version mismatch between the WSUS server API version: 3.2.7600.256 and the WSUS client API version 6.3.9600.16384.

Here's an article that goes over this behavior, and provides a workaround.

Using Patch Manager and WSUS in a mixed OS environment

David, that article is incomplete (broken links and incomplete information).

Is there an updated article for 2017?

Background:
Patch Manager uses Microsoft's API for WSUS to 'publish' the third party updates into the WSUS environment.

The publishing process that Microsoft designed requires a WSUS Server with a WSUS console (to publish to) and the server that is being published from (in this case, the Patch Manager server) with a WSUS console installation (full WSUS is not required on that box...just the WSUS Console piece).

The problem:  For the publishing process to work, the two WSUS consoles that exist on the Patch Manager server and the WSUS Server need to have matching versions.   If one is on Server 2012R2 and the other is on Server 2008R2, those console versions will never match.

Solution 1:  Install Patch Manager on a Server 2008R2 box (potentially even on the WSUS server itself) or Install WSUS on Server 2012R2.

Solution 2:  Install a Patch Manager Automation Server role (only) on the WSUS server or on another 2008R2 box.   You would then configure an Automation Server Routing Rule that would, essentially, tell Patch Manager to use that Automation Server to do the publishing instead of the default one on the main Patch Manager server.

I'm assuming the broken link you refer to is the KB4328 link; here is the page that is referring to:   Message: Failed to publish packageName. Publishing operation failed because the console and remote server versions do no…

Is this true even in a slight version difference? I'm getting the same error when the WSUS Server API we are running is version 6.3.9600.18324 and the client is 6.3.9600.17477. How would I update the client in this case?

Hello zdavid, your case is covered on Case 1 in the KB article that Kelly linked to:

https://support.solarwinds.com/Success_Center/Patch_Manager/Message%3A_Failed_to_publish_packageName._Publishing_operati…

There are two "flavors" of API mismatch.  The body of his message breaks down your options for Major version mismatch (3 vs 6).  For minor version mismatch, the short answer is:  Windows Updates.

The steps break down manually comparing, but sometimes it's as simple as one machine was updated and the other wasn't, so make sure to update the lower version server and that should resolve the issue.