A declarative sentence simply states something and tells you information. They don't ask a question nor are they an exclamation or a command. This sentence is a declarative because it tells you the baby snored while the mom rocked in the chair. All choices 1-4 say declarative, so you can't narrow anything out.
An intransitive verb is a verb that doesn't not need a direct object. That means something doesn't have to receive the action of the verb. A linking verb connects a subject and its predicate (something that tells what a subject is/tells more about a subject). A linking verb isn't an action. The verbs in the sentence are "snored" and "rocked." These are intransitive because (1) they are an action, so they can't be linking and (2) you can say "the baby rocked" and "her mom rocked" without needing an object. That means you can narrow out answers 3 and 4.
Finally, you have to choose between complex or compound. A complex sentence has at least one independent clause (can stand by itself as a sentence) and one dependent clause (can't stand by itself, usually modifies or provide more information for an independent clause). Clauses in complex sentences are usually connected with a subordinating conjunction. A compound sentence is created using two independent clauses (stand-alone). Clauses in compound sentences are usually connected with a coordinating conjunction, semicolon, or colon. This sentence is a complex sentence because it has one independent clause, "the baby snored quietly," and one dependent clause, "while her mom rocked in the chair." "While" is the subordinating conjunction.
