Can we convert ethanol to propanenitrile in the following way

CH3-CH2OH +HBr------PEROXIDE---> CH3CH2Br + H2O

​CH3CH2Br ----aq.KOH/KCN--------> CH2CH2CN + KBr


Method given by you is correct but the reaction conditions are wrong. In first reaction you have used peroxide which is wrong instead of it there should be ZnCl2 and in the second reaction which is nucleophilic substitution reaction alcohlic solution of KCN is used not aqueous solution. The reaction will be as follows:
CH3CH2OH   +   HBr    ZnCl2  CH3CH2Br   +   H2O

​CH3CH2Br  +   alc.KCN   →    CH3CH2CN   +   KBr

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