Symptom
Nothing happens when clicking "Select destination". The list of available locations for storing the backup does not open.
Cause
Known issue in build 10410 of Acronis True Image 2018 on Windows.
Solution
The issue has been fixed in build 10640, please update to the latest build.
As a temporarily solution without updating, click anywhere else outside of the "Select destination" text box. The clickable area is marked with green: