Problem installing apps in 4th generation iPod touch
The current available public version is iOS 12.3, with iOS 13 due for release soon. iPod touch 4th generation can't update past iOS 6.1.6, and it is not possible to install iOS 9 on it.

iOS 6 is pretty ancient and not a lot of 3rd apps support it. There has been major design changes starting with iOS 7, and architectural enhancements in later versions of iOS. Most 3rd party apps go as back as supporting iOS 9 and later. You are restricted to running the stock Apple apps and a very limited number of 3rd party apps that support running on iOS 6.