I don't think you have to think about delay
Considering that the async counter is simply an UP counter, we'll have to check at what o/p the CLR is activated
From the diagram: CLR = Q3' + Q0'
Only when Q3Q2Q1Q0 = 1001, CLR = 1' + 1' = 0+0 = 0
Whenever CLR is 0 all FFs will be reset
Thus, it can count from 0 to 8 i.e. mod 9