I think this quote represents the demons or bad things in life. In chapter eleven Enzo is left at home for several days. On the second day he hallucinated that a zebra stuffed animal in Zoe's room came to life and destroyed her stuffed animals. After the family comes back they see that the stuffed animals are ripped and broken and blame Enzo. Enzo believes the zebra destroyed the animals and then himself to frame Enzo. From then on, Enzo references the zebra throughout the rest of the book as a sort of evil or demon that comes and makes things bad and makes bad things happen. When he says the quote, it's after Eve was yelling because Zoe wouldn't eat and she says she doesn't want to be so mean. This can be interpreted as either Even being mean or Eve's cancer on a whole.
I think this quote means if you know where you want to go or where you are going you can get there. This makes sense because your will or want are your eyes and the place you're looking is where you want to go. If you, as the car, know where you are going you will be able to get there. This applies to the story not only because Denny is a race car driver but because Enzo believes when he dies he will return as a human. That is where his eyes are, looking at when he becomes a human. He is going that way. He is close to death and ready to leave his life as a dog.
The first quote is from when Denny takes Enzo around the race track for the first and last time. Denny tells him to bark twice if he wanted to go faster. Then when they neared the end Denny told Enzo theyd go on one more lap. Enzo loves this moment and remembers it often. He wants to go back on the track again. He wants to go one more lap and go faster and have more fun. The second quote is the last line from the last chapter where Enzo is a dog. Enzo is dying. He comes to terms with this and his last thought is the memory of going around the track. He wants one more lap with Denny. More time because he's dying. He knows he will return as a human but when it happens he wants more time, as most dying people do. He wants another lap with Denny where it's faster and more fun. His last thought is asking for more time.
Eve is dying. Before she hadn't come to terms with this and she was desperately hoping to stay alive. She had Enzo stay by her when she slept to protect her. Now, she has accepted she'll almost definitely die and she's ready. She tells Enzo she isn't scared to die, she isn't scared of her illness anymore. She tells him she doesn't need his protection anymore because she is ready. Eve tells Enzo that death isn't the end, something Enzo has known for a while, and tells him that this is why she isn't scared. Because she isn't ending.
From what Enzo tells the reader we know that Dennys dad never really supported him and his parents weren't good parents. Some of it has to do with the fact that Dennys mother is blind but that's not all of it. Now, Denny is going through a horrible time. He has no money and is losing the suit for his daughter. He calls his parents and invites them over to meet Zoe. They love her. Before they leave Dennys dad hands him money and tells him that this is for him to use to help with the law suit and his life in general. This makes some things better. It patches the bridge and now they can maybe fix their relationship.