Final answer:
The most appropriate management would be cognitive-behavioral therapy (CBT), which has been shown to be effective in treating insomnia. Medication should be used sparingly and seeking professional treatment is advisable.
Step-by-step explanation:
The most appropriate management for a 38-year-old male with an 8-week history of insomnia and irritability would be cognitive-behavioral therapy (CBT). CBT has been shown to be quite effective in treating insomnia and involves techniques such as stress management and behavioral changes that can contribute to better sleep. It is important to note that medication should be used sparingly as it can lead to dependence and alter the sleep cycle. If the symptoms persist and affect the patient's quality of life, seeking professional treatment from a healthcare provider experienced in treating insomnia would be advisable.