I'm sorry your uncle has liver cancer. Some people are not too close to their uncles, but I'm guessing from your question that you are fairly close to yours. Unfortunately, liver cancer is normally fatal, having one of the lowest survival rates of any cancer, and like other cancers, it is more difficult to survive the older one is. My grandpa had liver cancer, which was diagnosed last Februrary, and he passed away in September, about seven months after he knew he had liver cancer. He was 81.
There are two ways one can have cancer in the liver. The cancer could either have started there or could have spread there from somewhere else. When it starts in the liver, it's called "primary" liver cancer or "Hepatocellular Carcinoma". In this case, some liver cells become cancerous and form a growing tumor composed of cancerous liver cells. Primary liver cancer is actually quite rare in the USA and other developed nations, but my grandpa had primary liver cancer. Also, it's the most common cancer in Third World nations of Africa and Asia. Primary liver cancer is usually caused by eating moldy grains and peanuts (not a common problem in Western nations like the USA), Hepatitis B or C, or liver damage from alcoholism.
In the Western world, cancer in the liver is usually caused by cancerous cells that travel to the liver from somewhere else in the body, such as the colon. This is called "metastases". Metastatic cancers are difficult to treat because they are not just in one place, but liver cancer is bad whether it spread to the liver or started there.
Various treatments are available for liver cancer. If the tumor isn't too large, it's possible that the tumor can be surgically removed. The liver has an amazing ability to regenerate itself if a part of it is surgically removed, but if the cancer is too spread out within the liver such that the cancer cannot be completely removed without removing too much of the liver, surgical tumor removal (called "resection") is not an option. Some tumors can be killed with super cold temperatures (using a specialized probe), injections of alcohol directly into the tumor, and something called "radiofrequency ablation", which is something that basically microwaves the tumor. Whether any of these options is possible depends a lot on how far along the cancer is when it is detected. If the cancer has had too much time to grow, any treatment option the oncologist (cancer doctor) is able to offer will probably only help to relieve pain and help to extend life expectancy rather than cure the cancer. If the cancer can't be removed or otherwise destroyed by some method, it will eventually take over the liver, and as the liver function decreases, the person becomes weaker and weaker before passing away.
Again, I am sorry about your uncle. If the cancer isn't too far along, he might survive the cancer, but to be honest, liver cancer is normally fatal whenever it is diagnosed. If and when you find out that his cancer is terminal, you should do whatever you can to show your uncle love and care and think about what you need to say before you lose him. I also recommend praying for him if you believe in prayer, which I myself do. It's a tough thing to deal with, so I wish you and your family all the best.