I'm thinking...If some cheater or hacker got ban by PunkBuster in Battlefield 4 server, Can They just use different IP enter the same server?
A different IP means a different computer, or if they changed their IP, the system believes it is a new computer; unless they have a system to detect otherwise.
So to answer your question: Accounts get banned by PunkBuster. But if they were to ban just an IP; someone could easily change it. Only accounts get banned, not IPs.
As the other user stated, technically yes, it's possible to change ip.
There is a difference between internal and external ip. Your provider might give you 1 public IP, this is what you use to go online. While inside you can have over 200 different IP's.
When you play online you are using that 1 public ip, so when you connect the server can see that you connected with that ip. There is some explanation needed for internal and external ip:
Your external and internal ip sortof get fused to send a message to the server, because your brother or sister could also be online at the same time, yet have a different LOCAL ip.
If they only banned the ip, you could go and change the ip to play. But i guess they either ban on MAC-address (The physical address of your pc which cant be changed) or they ban the account linked to ip or something.