HOW WAS GULLIVE GAIN THE FAVOUR OF THE MAGISTY AND THE COUNCILAR MINISTER IN LILLIPUT?

Even though soldiers are taunting him Gulliver treats them fairly well (shoves them in his pocket). The Emperor hears this and responds with kindness. Gulliver builds things for them. Finally Gulliver earns his freedom by agreeing to follow all rules, especially in times of war (he's going to be used as a weapon).