Cimrman pochválil Čechovova kniha povídek.

The main verb is "pochválil" 3sg. past tense form of pochválit 'to praise.'

The subject is 3sg masc., so Cimrman qualifies for it.; Čechovova kniha does not. Instead, Čechovova kniha should be the direct object, i.e. accusative case.

Povídek is a gen. pl. form of povídka; this form fits well in the sentence since it can be considered to further specify Čechovova kniha, i.e. "Chekhov's book OF stories."

Note that "Čechovův" (Chekhov's) that modifies "kniha" declines like a noun (in this case feminine žena-type) in the nom. and acc. cases.