As it can be seen from the circut, there is no single clock operating all the flipflops hence it's not a synchronous counter. Clock signal is only given to the First Flip Flop.
Therfore, first two options are eliminated.
Assume that, initally all flip-flops are reset. Following is the output sequence:
QA QB QC
0 0 0
0 0 1
0 1 0
.
.
1 1 1
It's counting UP from 0 to 7, if it was mod 8 down counter, it will count from 7 to 0.
Hence, it's an Asynchronous mod 8 UP counter!