Symptoms

K2 BP and SF compatibility matrices say that we do not support .NET 4.6 for any version of K2 older than 4.6.11.
But it may be not 100% clear whether K2 does not support (and requires not to install) .NET 4.6 on SharePoint 2013 server used in K2 4.6.9 environment. For example if the following components are installed on the SharePoint 2013 server:

K2 blackpearl Setup Manager 4.6.9
K2 Core 4.6.9
K2 for SharePoint 2013 in SharePoint 2010 mode 4.6.9

Is it necessary not to install .NET 4.6 on such server?
 

Diagnoses

In order to have fully supported K2 4.6.9 environment you should not install .NET 4.6.9 on any servers where K2 components are installed. Please refer to K2 compatibility matrices for details on supportability and compatibility whenever you plan any upgrades in your K2 environment.

Please refer to links below to access product specific compatibility matrices:

http://help.k2.com/blackpearl/support-matrix
http://help.k2.com/smartforms/support-matrix
http://help.k2.com/connect/support-matrix
http://help.k2.com/appit/support-matrix
 

Resolution

K2 4.6.9 (and any other version older than 4.6.11) components are not compatible/tested with .NET 4.6, consequently .NET 4.6 should not be installed on any server which has K2 components installed on it. In case .NET 4.6 is a requirement K2 components has to be upgraded to 4.6.11 or newer version.