[Modules] Show that $h_3$ is injective given comutative diagram

Let $R$ be a ring with $1$. Consider the comutative diagram of $R-modules$ with exact lines attached.
Show that if $h_2$ and $h_4$ are injective and $h_1$ is surjective, then $h_3$ is injective.

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  • Hey, gareat job! Would you be able to answer the other question I asked about modules?

  • I think I have seen that question some time ago, but I cannot remember how to solve it now. Someone more proficient in algebra than me should take it.

The answer is accepted.