What comes first width by height or height by width when defining a picture frame?

Width will normally go first. Think of it this way: A piece of paper is usually 8.5 inches by 11 inches if looked at it by a portrait, not landscape so therefore, which one is the height? Yes, the second one.

Another example would be map and graph coordinates where you quote the x axis value (the width) before the y axis value (the height).