Say I have part 1, and part 2. I want to use the CFrame.new constructor to have part 1 look at part 2, which I know how to do. However, I only want part 1 to look at part 2 without rotating up or down. How can I achieve this?
After you set the CFrame, you can just set the X (or Z IDK which) components of the Orientation of the part to 0:
part.Orientation = Vector3.new(0, part.Orientation.Y, part.OrientationZ)