If I purchase a PS4 console with online games already bought and want to use my own PSN account, will I lose the games?

I am buying a secondhand PS4 from someone and they have a PSN account that has purchased 20+ games with 6 months left on the online status.

I want to know if I will lose the games after 6 months when I switch to my own PSN account?

Yes you will. Games purchased through the PSN Store are owned by the account which purchased them. If you swap accounts, you will lose access to those titles.

You can login with the owning account and set the system to their primary ps4, which will allow some sharing of the titles. However, once their PSN runs out, you will lose access to the PS+ titles.

IGN have a guide on sharing.

1. Login with your account on your family/friend's PS4
2. Go to the "Settings" tab
3. Go to "PSN" Click on "Activate as Your Primary PS4"
4. Click "Activate"

Now they should be able to use your downloads on their PS4. They don't have to login to your account to play your games or use your PS Plus.