Bacterial Infection: This is the most likely diagnosis due to the elevated neutrophil count, which is a common response to bacterial infections. The high monocyte count may indicate a chronic or severe infection.

Chronic Inflammatory Disease: Conditions such as rheumatoid arthritis, lupus, or inflammatory bowel disease can cause an increase in both monocytes and neutrophils due to chronic inflammation.
Viral Infection: Some viral infections, like influenza or COVID-19, can cause an increase in monocytes and neutrophils, although this is less common than bacterial infections.
Acute Stress or Trauma: Severe stress or trauma can cause an increase in white blood cell count, including both monocytes and neutrophils, due to the body's stress response.

Sepsis: Although less likely, sepsis is a life-threatening condition that can cause an elevated WBC count, including high monocyte and neutrophil counts. It is crucial to consider sepsis in patients with a high WBC count, especially if they have symptoms such as fever, hypotension, or organ dysfunction.
Leukemia: Certain types of leukemia, such as chronic myeloid leukemia (CML) or acute myeloid leukemia (AML), can cause an elevated WBC count, including high monocyte and neutrophil counts. Although rare, leukemia is a potentially life-threatening condition that requires prompt diagnosis and treatment.

Myeloproliferative Neoplasm: Conditions such as polycythemia vera or essential thrombocytosis can cause an increase in white blood cell count, including monocytes and neutrophils, although this is relatively rare.
Histiocytosis: Rare conditions such as Langerhans cell histiocytosis or Erdheim-Chester disease can cause an increase in monocytes and neutrophils, although these conditions are extremely rare and usually present with other distinctive symptoms.