Learn Hardcore German: Ich lege einen Brief in den Briefkasten.

Brief is a masculine noun and here functions as the direct object of legen, so it takes the accusative case. The correct masculine accusative indefinite article is einen, not ein.

Why is it in den Briefkasten instead of im Briefkasten?

You’re expressing movement into the mailbox. With the preposition in, movement triggers the accusative case (hence den). im is the contraction of in dem (dative) and indicates a static location rather than motion.

Can I contract in den to ins Briefkasten?

No. ins is the contraction of in das (used with neuter nouns). Since Briefkasten is masculine (der Briefkasten), you must use in den, which does not contract to ins.

Why is the preposition in used here and not auf or an?

You’re placing the letter inside an enclosed container.

in = into (an enclosed space)
auf = onto (on top of)
an = to/against (on the side of)

Since the letter goes into the mailbox, in is the correct choice.

Why do we use legen? Could I use stecken or werfen instead?

German distinguishes different placement verbs:
• legen – to lay something down horizontally (perfect for a flat letter)
• stecken – to stick or insert into a slot
• werfen – to throw

All three are grammatically correct here but change the nuance:
• Ich lege einen Brief in den Briefkasten. (careful placement)
• Ich stecke einen Brief in den Briefkasten. (insertion)
• Ich werfe einen Brief in den Briefkasten. (tossing)

Could I say hineinlegen instead of lege ... in?

Yes. Ich lege einen Brief in den Briefkasten hinein is perfectly fine. hinein reinforces the inward motion, but it’s optional—in den already indicates direction.

Why is Briefkasten one word and capitalized?

German forms compound nouns by concatenating words: Brief + Kasten = Briefkasten. Additionally, all German nouns are always written with an initial capital letter, so Briefkasten naturally begins with a capital B.