It is a colon
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It's not a simple sentence: it has more than one clause.
It is also not compound: the two clauses are not independent <span>and a compound has independent clauses.
</span>It is however complex: the two clauses are not independent (<span>While you were on vacation is the dependent clause). This is the correct answer.
(it's not compound-complex because it has 2 and not more clauses)
</span>
That is because of the connotation. The denotation for house and home is a place of residence, however, our minds perceive the word house as neutral and generic while home is something that is close to us and brings us safety and security. That is an advertising ploy.
