Final answer:
The patient's symptoms and chest X-ray findings suggest bronchiectasis as the most likely diagnosis.
Step-by-step explanation:
Given the patient’s history of recurrent cough with sputum production since childhood, the presence of fever, grade III finger clubbing, rales on auscultation, and a honeycomb appearance on chest X-ray, the most likely diagnosis is bronchiectasis. Bronchiectasis is characterized by permanent dilation of the bronchi and bronchioles, caused by chronic infection and inflammation. The symptoms of chronic cough and the production of purulent sputum, along with clubbing, are indicative of bronchiectasis rather than the other conditions listed such as COPD, tuberculosis, pneumonia, or cystic fibrosis, which tend to present differently.