Acute Bronchitis: This is the most likely diagnosis given the patient's symptoms of cough productive of green sputum for 8 days. Acute bronchitis is a common condition characterized by inflammation of the bronchial tubes, often caused by a viral infection, but can also be bacterial. The green sputum suggests a possible bacterial component or secondary bacterial infection.

Pneumonia: Community-acquired pneumonia (CAP) is a significant consideration, especially in an elderly patient. The presence of green sputum could indicate a bacterial pneumonia, which would require antibiotic treatment.
Chronic Obstructive Pulmonary Disease (COPD) Exacerbation: If the patient has a history of COPD, an exacerbation could present with increased cough and sputum production. The green color of the sputum might suggest a bacterial infection triggering the exacerbation.
Asthma Exacerbation: Although less common in a new presentation at 78 years old, an asthma exacerbation could present with cough and sputum production, especially if the patient has a history of asthma.

Pulmonary Embolism: Although less likely to present with green sputum, pulmonary embolism can cause cough and should be considered, especially if there are other risk factors such as recent immobilization, cancer, or signs of deep vein thrombosis.
Lung Cancer: In an elderly patient, new onset of cough with sputum production could be a sign of lung cancer, especially if there's a history of smoking.
Tuberculosis (TB): While less common in many areas, TB can present with chronic cough and sputum production. It's a critical diagnosis not to miss due to its public health implications and the need for specific treatment.

Cystic Fibrosis: Extremely rare to present for the first time in an elderly individual, but could be considered if there's a history suggestive of untreated cystic fibrosis.
Bronchiectasis: This condition involves permanent enlargement of parts of the airways and can cause chronic cough and sputum production. It might be considered if the patient has a history of recurrent infections or other suggestive symptoms.
Aspiration Pneumonia: If the patient has risk factors for aspiration (e.g., dysphagia, neurological disorders), aspiration pneumonia could be a rare but important consideration, especially if the sputum is foul-smelling or if there are signs of aspiration on imaging.