Chronic Liver Disease: This is the most likely diagnosis due to the combination of elevated liver enzymes (ALT and alkaline phosphatase) and low albumin, which is a common finding in liver cirrhosis or chronic liver disease. The liver's decreased ability to synthesize proteins like albumin, along with the elevation in liver enzymes indicating liver damage, points towards a chronic liver condition.

Viral Hepatitis: Both acute and chronic viral hepatitis can cause elevations in ALT and alkaline phosphatase. Low albumin can be seen in more severe cases, especially if there's significant liver inflammation or cirrhosis.
Alcoholic Liver Disease: Similar to chronic liver disease, alcoholic liver disease can cause a range of liver enzyme abnormalities and decreased albumin production due to liver damage.
Non-Alcoholic Fatty Liver Disease (NAFLD): NAFLD, particularly in its more severe form known as non-alcoholic steatohepatitis (NASH), can lead to elevated liver enzymes and, in advanced cases, cirrhosis with associated low albumin levels.

Budd-Chiari Syndrome: A condition characterized by the obstruction of the hepatic veins, which can lead to liver dysfunction, including elevated liver enzymes and low albumin. It's crucial to consider this diagnosis due to its potential for severe complications if not promptly treated.
Wilson's Disease: An inherited disorder that leads to copper accumulation in the liver, causing liver damage. It can present with elevated liver enzymes and low albumin, among other symptoms. Missing this diagnosis could lead to severe and irreversible liver damage.
Autoimmune Hepatitis: An autoimmune condition that causes the body's immune system to attack liver cells, leading to inflammation and liver damage. It can present with a wide range of liver enzyme abnormalities and decreased albumin production.

Alpha-1 Antitrypsin Deficiency: A genetic disorder that can cause liver disease due to the accumulation of abnormal alpha-1 antitrypsin protein in liver cells. It's a rare condition but should be considered in cases where common causes of liver disease have been ruled out.
Glycogen Storage Diseases: Certain types of glycogen storage diseases can affect the liver, leading to abnormalities in liver function tests, including elevated enzymes and low albumin. These are rare genetic disorders that affect glycogen metabolism.
Cystic Fibrosis: While primarily known as a respiratory condition, cystic fibrosis can also affect the liver, leading to focal biliary cirrhosis and, in some cases, multilobular cirrhosis, which could result in elevated liver enzymes and low albumin.