Since you are referring to Adobe Illustrator, we can assume you are working with (mostly?) vector artwork, in which case ignore any dpi information. Or better yet, use the default 300dpi you get when creating a new AI document. This 300dpi setting only applies to raster elements being used in your artwork (pictures vs. shapes).
Then, when you export from AI to PDF, there is a 'Compression' tab in the export panel where you can set a higher dpi count (600 if you want to), but this again only affects the photos you are using in your document.
Since you are just learning you might not be aware of all the differences between AI and PS, so in case you are just mixing photos together, then yeah do it in Photoshop at 600dpi if they told you so (after you read this).