**Core Concept**
The question is testing the ability to recognize and diagnose a condition that affects the mental health of an individual experiencing significant stress or emotional turmoil, specifically in the context of a family crisis.

**Why the Correct Answer is Right**
The father's symptoms of sleep deprivation, lethargy, headache, and low mood, in the context of his son's leukemia diagnosis, are suggestive of a major depressive disorder (MDD). The diagnostic criteria for MDD include a persistent feeling of sadness or loss of interest in activities, significant weight loss or gain, insomnia or hypersomnia, fatigue or loss of energy, feelings of worthlessness or guilt, difficulty concentrating, and recurrent thoughts of death or suicidal ideation. The father's interactions with others and work absence also indicate a significant impairment in social and occupational functioning.

**Why Each Wrong Option is Incorrect**

* **Option A:** This option is not provided, so we'll move on to the next one.
* **Option B:** While anxiety disorders can present with similar symptoms, they typically involve excessive worry or fear about specific situations or objects, which is not mentioned in the scenario.
* **Option C:** Adjustment disorder with depressed mood is a possible diagnosis, but it would typically require a shorter duration of symptoms (e.g., up to 6 months) and a more significant impact on social or occupational functioning than described.

**Clinical Pearl / High-Yield Fact**
When diagnosing depression in the context of a family crisis, consider the presence of significant stressors, such as a loved one's serious illness, and the individual's response to those stressors. This can help differentiate between adjustment disorder and major depressive disorder.

**Correct Answer: C. Adjustment disorder with depressed mood**