Can my Apple Watch Nike series 4 pair with Iphone 12 mini ?

The person that you bought this watch from needs to follow all the steps in this link;

Remove the Activation Lock so that the buyer can use it.

If they can't or won't then get your money back or recycle the watch and put it down to experience.

Yes, they are compatible

A series 4 watch was discontinued a long time ago,sounds like it's still paired to another phone and it will have an activivation lock on it;

About Activation Lock on your Apple Watch

What version of iOS is on your iPhone?

Did you unpair the watch from your old phone,you can only pair a watch to one phone at a time.