Complex sentence: Before his post at the United Nations, Meyer was at Newsweek Magazine for two decades, most recently (2001--2007) as Europe Editor for Newsweek International, where he also oversaw the magazine's coverage of the Middle East and Asia.
Split into simpler sentences: Before his post at the United Nations, Meyer was at "Newsweek Magazine" for two decades. From 2001 to 2007 he was Europe Editor for "Newsweek International", where he also oversaw the magazine's coverage of the Middle East and Asia.