Given JK FlipFlop, For J=0 and K=0,FF nextstate = previous state
Initally QA = 0,QA' = 1
so UP counter is initated and Q1 Q0 = 00 ,01,10,11
Now when 11 is seen, Y3 = (Q1.Q0)' = 0 occurs
As preset is active low as soon as Y3 input of preset is 0,preset takes place.
This preset sets the value of QA = 1, thus Now DOWN counter takes place
The count sequence of down counter is 10,01,00
Again same sequence repeats as above
Here we want only output when 8 clock pulses are applied so 0,1,2,3,2,1,0,1.