My friend asked me to meet him outside the cinema . . . . . . . . an hour's time.

The correct answer is B: in.

Let's break down why:

The Question Meaning:
The sentence means your friend wants to meet you after a duration of one hour from now.

Why "in" is correct:
"In" is used to express a point in the future *after* a certain duration of time.
For example, "I will be there in an hour" signifies that you will arrive one hour from the current time.

Why the other options are incorrect:
"on" is generally used for specific dates or days (e.g., "on Monday").
"at" is used for a specific time or location (e.g., "at 5 PM" or "at the park").
"within" indicates a limit or range of time. If you said "within an hour", it would mean sometime *before* or *at* one hour.
Therefore, "in" is the most suitable preposition for expressing a future point after a time duration of one hour.