Things to notice:
1) Given clock is +ve edge triggered whereas the flipflops are negative edge triggered.
2) Presets when active sets the flipflop value to 1 unlike resets which sets it to 0.
3) Pr0,Pr2 initial values are 0,0.
4) Pr1 will become 0 when Complement(clk.Q0.Q2) = 0
(Q0,Q1,Q2)
(000)
(100)
(010)
(110)
(001)
(101)
(011)
(111)
(000)
Complement(clk.Q0.Q2) = 0 after 5th clock pulse at (1,0,1) and Q0 is changing from 0 to 1 which indicates the cycle is +ve edge triggered.
At this point flip flops values will be reset to 111
So the possible values are (000) -> (100) -> (010) -> (110) -> (001) -> (111) -> (000), so the mod is 6.