To do it through the Transformation constraint, set your constraint this way (image below). Essentially, in the constraint, choose your controller object as Target, click on Rotation for both Map From and Map To. Under Map To, as you want X to control the Y rotation, choose Y Source Axis > X, choose the degree amplitude, you can set to -10° and 10°, for ...


2 cubes Right mouse click on y-rotation > add driver choose these settings and you get:


This is easy: Ctrl + A ⇾ Apply Rotation Noted, that has been already answered in comments, so mark them as wiki


You have delta transforms: To clear deltas, press Alt+R(G, S) → F9 (Adjust last operation) → Clear delta If you want to keep current position, I could recommend press Ctrl+A → rotation, then Alt+R → F9 → Clear delta to rotate back.

Only top voted, non community-wiki answers of a minimum length are eligible