Horace Danby was suffering from hay fever.

Explanation:

Hay fever, also known as allergic rhinitis, is a common allergic condition that occurs when the immune system overreacts to allergens in the environment. It is characterized by symptoms such as sneezing, itching, runny nose, and nasal congestion. In Horace Danby's case, he exhibited symptoms that align with hay fever, making it the correct answer.

Symptoms of Hay Fever:
1. Sneezing: Horace Danby's sneezing could be a result of hay fever. Sneezing is one of the most common symptoms of this condition.
2. Itching: Itching of the nose, eyes, and throat is another common symptom of hay fever. If Horace Danby experienced itching, it further supports the diagnosis of hay fever.
3. Runny Nose: Hay fever can cause a clear, watery discharge from the nose, which could explain Horace Danby's symptoms.
4. Nasal Congestion: Hay fever can also lead to nasal congestion or a blocked nose. If Horace Danby had difficulty breathing through his nose, it could be due to hay fever.

Why it is not other options:
a) Cold: While some symptoms of hay fever may overlap with a common cold, hay fever is typically caused by allergic reactions rather than viral infections.
b) Cough: Coughing is not a prominent symptom of hay fever. It is more commonly associated with respiratory infections or other conditions affecting the lungs.
d) Teeth ache: Toothache is unrelated to hay fever. It is typically caused by dental problems, such as tooth decay or gum disease.

In conclusion, based on the symptoms presented by Horace Danby, it is evident that he was suffering from hay fever. Hay fever is an allergic condition characterized by symptoms such as sneezing, itching, runny nose, and nasal congestion.