Adobe Campaign uses an embedded web servlet called Apache Tomcat to process HTTP/HTTPS requests between the application and any external interface (including Client Console, tracked URL links, SOAP calls, and others). There is often an external web server (usually IIS or Apache) in front of this for any external-facing Adobe Campaign instances.
Learn how to find out the current version of embedded Tomcat web servlet used in an on-premise instance of Adobe Campaign here: Locating Tomcat Version
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This is a really good and correct way.
There is another way (execute as neolane user) which is faster and can show current version:
cd tomcat_folder/lib java -cp catalina.jar org.apache.catalina.util.ServerInfo