Well, both a monologue and a soliloquy are spoken by one person, right? So, you can discount the third answer right away. (A soliloquy is not a dialogue.)
The first response is correct. Let's look at the others to see whether there is something more correct, more exact.
Hmmmm, the second response is the exact opposite, and that is incorrect. Think about the words "solitary" or "solitude" — they're related to "soliloquy." All these things refer to being alone.
We've already tossed out the third.
The fourth . . . look at how it's the same, and how it differs, from the first. Is a monologue a speech "given by one characters to other characters"? Or is it a speech "made in the presence of other characters"? Is a soliloquy spoken by someone "thinking aloud" or is it speech made when the character is alone? Well, the character is alone . . . but he is also thinking aloud. But he must first be alone. He cannot be thinking aloud in the presence of others.
So the last response is the better of the two. It is more accurate than the first, because it contains the essential aspect of a soliloquy — the character is alone.
