8051 code to use R4(LSB) and R5(MSB) as a single 16bit counter, and increment the pair untill number is FFFFh

Logic is too simple. For better understanding, I would suggest you something. Use a scientific calculator and in hex mode go on adding 0x01 each time. And then study my code. You will have a better understanding.

ORG 000h
MOV R4,#00h
MOV R5,#00h

main:
         INC R4
         CJNE R4,#0FFh,main
         CJNE R5,#0FFh,end  ; Observe this line carefully and think after it 
         INC R5
         MOV R4,#00h

end: NOP

END