Get Roy to train you and you will certainly become the best boxer in the town. However, it is not so easy to do. He seems to be unbothered and talking with him doesn’t seem to bear the fruit. He will ask you to make various things for you, but you can gain his respect only if you think smarter.
Fix Toy Car is the quest that you need to overcome. There is an old and damaged car that you need to repair somehow. Its engine is lying nearby and you can make an attempt to do something about it. Although, all you can do about it is to smash the engine. But this is perfectly fine for Roy, as he will thank you for your help!
Then all you have to do is to talk with your friend and he will suddenly agree to your offer. As a bonus, you can sit with Roy and drink a bottle of beer. Meet him at the gym to continue the training.