Dual-energy X-ray absorptiometry (DEXA) is a medical imaging technique that is primarily used to measure bone density. This non-invasive procedure uses low-dose X-rays to scan specific areas of the body, most commonly the spine and hip.

Option 1, the spread of solid tumors, is not assessed by DEXA. This technique is specifically designed to measure bone density and is not effective in detecting or monitoring the spread of tumors.

Option 3, the detection of ulcerous growth in the stomach, is not within the scope of DEXA. This imaging technique is not used to visualize or diagnose abnormalities in the digestive system.

Option 4, the measurement of the extent of brain hemorrhage, is also not applicable to DEXA. This technique focuses on bone density and is not used to assess brain hemorrhage or any other brain-related conditions.

Therefore, the correct answer is option 2, bone density. DEXA is commonly used to diagnose osteoporosis and assess the risk of fractures by measuring bone density in specific areas of the body.