Partial ordering and union of chains

Question

I’ve just started a logic course and I came across this problem.

Let $P,\leq_p$ be a partial ordering, and let $k$ be a positive integer.

1. Use the Compactness Theorem to show that $P$ is the union of $k$ chains if and only if each finite subset of $P$ is the union of $k$ chains.

How can I prove that if $P$ is the union of $k$ chains then each finite subset of $P$ is the union of $k$ chains.