Hello kaanthdotcom,
Ensuring your iPod shuffle (4th generation) is recognized by your PC to sync music is important and you've come to a great place for help! If your iPod isn't recognized by your PC you'll want to complete the steps listed below to resolve the issue. You can also find these steps outlined in the following article.
1: "Make sure that your iOS or iPadOS device is turned on, unlocked, and on the Home screen.
2: Check that you have the latest software on your Mac or Windows PC. If you're using iTunes, make sure you have the latest version.
3: If you see a Trust this Computer alert, unlock your device and tap Trust. If you can't unlock your device because you forgot your passcode, find out what to do.
4: Unplug all USB accessories from your computer except for your device. Try each USB port to see if one works. Then try a different Apple USB cable.*
5: Restart your computer
6: Restart your iPhone, iPad, or iPod touch.
7: Follow these additional steps for Mac or Windows PC.
8: Try connecting your device to another computer. If you have the same issue on another computer, contact Apple Support."
If your computer doesn't recognize your iPhone, iPad, or iPod
While the title of the article and the steps reference other iOS and iPadOS devices, these steps are still helpful for the iPod shuffle (4th generation). If you continue to have issues after those steps, reaching out to Apple as outlined in step 8 is the right next step. You can also find their contact details via the Get Support website.
Take care!