Again vs Back

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Although they may be used with similar meanings, they are a bit different from each other.

Back With a Verb

When back is used with a verb, it suggests a return to an earlier situation or it explains a movement in the opposite direction to an earlier one.

Take the car back where you bought it from.
I’m taking you back to the hotel.
You have five seconds to take your words back, or else I will hit you.

Again With a Verb

Different from back, again suggests repetition.

I loved that song, can you please play it again.
Your friend was a real headache the last time he came, so please don’t invite him again.
I promise I will never break your heart again.

Sell Back / Again

When you sell something back, you sell it to the same person or place where you bought it.

I didn’t like the pen you sold me, I want to sell it back to you.

Attention:

Don't say return it back to you... Say return it to you or sell / give it back to you

Call Back

It means either to return or repeat a phone call.

I don’t have time to talk to you now, please call me back later in an hour.

We Can't Use Back

When there is a verb suggesting the idea of return itself, we can’t use “back”

I will never return to you after all you did to me. (not…return back to you…)
I told you not to close the door, now open it. (not…open it back)

The Order in Sentence

Back can be used between a verb and its object if it’s not a pronoun, however we cannot use again in this way.

Take back your dictionary, I don’t need it anymore.
Note: (take your dictionary back) is also possible.
Play the guitar again please. (not play again the guitar.) ↑▲▲▲▲▲▲▲↑