Synchronizer uses multiple ports by default per its installation guide, for several reasons during the installation or after it some of these ports could be busy. Sometimes the it's the antivirus running in the Synchronizer server or even the System itself could make use of them.

Is there a way to change the default ports?

Under the following path check the file called bindings-jboss-beans.xml,

C:\Program Files\HPE\HPE ALM Synchronizer\jboss\server\default\conf\bindingservice.beans\META-INF

This file manages port binding, here you can update the Synchronizer port settings (except 7064 which can be changed from  HPE ALM Synchronizer\jboss\server\default\deploy\jbossweb.sar\server.xml).

NOTE: the paths could vary according to your Synchronizer version, the parent path could be HP, HPE or Micro Focus.

Make a backup of the files to be modified and stop the Synchronizer service prior to any change.