Help me beat my trainer

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Cheszzic

Hi! Me and my trainer FM Djorjde Konjevic (2324) played a few games (5 to be exact, which i lost all) and the final game we reached the position were we adjourned and left to be studyied home, sort of a part of a learning and i analysed the position and saw that it is a dead draw but if not played right for his side he loses by force, so could you analyse the position and tell me what could i or he get wrong in the position?

Im White

White: pawns on b2,a4,f4 king d4  bishop e5,  rook h8

Black: pawns d5,e6,f7, h6  king g4 rook h3,   bishop g6