Syncing iPod Touch won't return Apps

I just got an iPod Touch 2 days ago. For the first time I hooked it up to iTunes. All the 20 apps I downloaded on the iPod show up in "Apps" under "LIBRARY" but they won't go back to my iPod.

How do I get my apps back on to my iPod Touch? Selecting and syncing the iPod doesn't work!

 

Clarity for those with this same problem

I couldn't figure it out so I followed advice from a forum. The process given didn't work, but I found another way.

You have to select your iPod on the left menu, then select the "App" TAB on the top of the window....and THEN you check "Sync Apps" at the top there.