The block has two tendencies
(i) to slide w.r.t. plank
(ii) to topple over the point O maximum acceleration for sliding
`f_(s)=ma le f_(L)`
`ma le mu mg`
`ale g/3 , a_(max)=g/3`
maximum acceleration for toppling,
N=mg, `f_(s)=ma`
`N.(H/8)=H/2 f_(s) , a_(max)=g/4`
So, the block will topple before sliding. hence `f_(max) =(M+m) g/4`