Use a PC to rip your PS2 disc into an ISO format.
Connecting a modified PS4 to PlayStation Network (PSN) can result in a permanent ban of your account and hardware. Conclusion ps2 to ps4 pkg download
The PS4 does not natively play PS2 discs. Instead, it uses a software emulator. When you download a "PS2 Classic" from the PlayStation Store, you are essentially downloading a file that contains the original PS2 game code wrapped inside a PS4-compatible emulator shell. Use a PC to rip your PS2 disc into an ISO format