Translation:She would like to do something for him.
The way it was explained to me is that you use "gøre" for "make" when it's paired with an adjective, so for instance ...
Hun vil gerne lave noget for ham. = She will make something for him. Hun vil gerne gøre noget godt for ham. = She will make something good for him.
So because there's no adjective here, gøre doesn't mean "make".