The best way to approach this question would be to first define the four choices given. 

A soliloquy is a device used in a play to reveal a character’s inmost thoughts; the character speaks to him- or herself with total disregard to anyone who could be around to hear.

An English sonnet, also known as an Elizabethan sonnet or a Shakespearean sonnet, is a poem in iambic pentameter consisting of three quatrains and a couplet, with the rhyme scheme abab cdcd efef gg.

An elegy is a reflective, mournful poem or song, usually a dirge for the dead.

A lyric in this case, is a poem or song that expresses emotion.

Now, we know that the correct answer cannot be (A), because in this monologue the actor is not speaking to himself, but directly to the audience.  Neither is he revealing anything about himself, but rather telling everyone what is about to happen in the play. 

The monologue is very matter-of-fact, and expresses little emotion or reflection.  It is not mournful.  We can therefore eliminate (C) and (D).

And so we are left with the correct answer, (B), which is substantiated by the format of the monologue.  There are fourteen lines which follow the correct rhyme scheme for an English sonnet, and they are all written in iambic pentameter.  It meets all the requirements of form and meter, and therefore we can say that this monologue is indeed written as an English sonnet.