Explanation:

The correct answer is option 'A' - for.

When we talk about travelling for a few days, we use the preposition 'for' to indicate the duration of the trip. The preposition 'for' is used to express the length of time or duration of an action or event.

Here is a breakdown of the options and why option 'A' is the correct answer:

a) for:
- This preposition is used to indicate the duration of the trip.
- It shows that the person will be travelling for a few days.
- Example: "Next month, I will be travelling for a few days."

b) by:
- This preposition is used to indicate the method or means of transportation.
- It does not provide information about the duration of the trip.
- Example: "Next month, I will be travelling by train."

c) in:
- This preposition is used to indicate a period of time or a specific point in time.
- It does not provide information about the duration of the trip.
- Example: "Next month, I will be travelling in the morning."

d) on:
- This preposition is used to indicate a specific day or date.
- It does not provide information about the duration of the trip.
- Example: "Next month, I will be travelling on Monday."

In conclusion, the correct answer is option 'A' - for. It is used to express the duration of the trip and indicates that the person will be travelling for a few days.