Light fixture is out is identical to the above photo, a hanging halogen light fixture. The previous owner told us to rotate the fixture by about 20 degrees and it should lower. I rotated the fixture but it didn't work - I'm worried that I damaged the fixture as it's now sitting slightly lower than before.
I doubt that you damaged the fixture. You probably loosened it from the electrical box it's attached to. Usually the bulbs can be changed without removing the fixture from the wall. Turn the light off (because it gets very hot) and try to push up the fixture and rotate it in the opposite direction to correct what you did before. Get a ladder, not a chair, and get up there close so you can see what's going on up there and where the bulbs are.