Adduce means to ‘offer as a reason in support of an argument; cite as pertinent, conclusive, or persuasive’. For example: “The speaker decided to adduce illustrations from real life on the subject of faith and religion.”, “We are not in a position to adduce forcible proofs for our argument/”
Deduce, on the other hand, means ‘to reach a conclusion by reasoning’. For example: “The police officer was able to deduce that the criminal was a man.”
Usage example that uses both these words: Because the lawyer was able to adduce an explanation for the theft, the judge was able to deduce who was responsible.