Αν ξεχάσω το τηλέφωνό μου, ξαναπάω σπίτι.

Because Greek often drops subject pronouns when they are not needed.

The verb ending already tells you who the subject is:

• ξεχάσω = I forget
• ξαναπάω = I go back / I go again

So Greek does not need εγώ here. You would only add εγώ if you wanted emphasis, contrast, or clarity.

Αν means if.

It introduces the condition:

• Αν ξεχάσω το τηλέφωνό μου = If I forget my phone

So the sentence has the structure:

• condition
  • result

That is very similar to English If..., ...

Ξεχάσω is the aorist subjunctive form of ξεχνάω / ξεχνώ.

After αν, Greek commonly uses a subjunctive-type form to talk about a possible event. Here, ξεχάσω presents the forgetting as one complete event:

• αν ξεχάσω = if I forget / if I happen to forget

If you used ξεχνάω, it would sound more like an ongoing or repeated situation, not a single complete act.

So:

• αν ξεχάσω = if I forget it on some occasion
• αν ξεχνάω = if I am forgetting / if I tend to forget

The version in your sentence is the natural one for a single act of forgetting.

Without θα, the sentence usually sounds more like a general rule, habit, or what I do in that situation:

• Αν ξεχάσω το τηλέφωνό μου, ξαναπάω σπίτι. = If I forget my phone, I go back home. = Whenever I forget my phone, I go back home.

If the speaker wanted to stress one future occasion, Greek would often use:

• Αν ξεχάσω το τηλέφωνό μου, θα ξαναπάω σπίτι. = If I forget my phone, I’ll go back home.

So the sentence you have sounds a bit more like a habitual reaction than a one-time future promise.

Ξανα- means again or back.

So:

• πάω = I go
• ξαναπάω = I go again / I go back

In this sentence, ξαναπάω σπίτι most naturally means I go back home.

Also, πάω is the common shorter form of πηγαίνω in everyday Greek. So ξαναπάω is basically the everyday equivalent of ξαναπηγαίνω.

In Greek, possessed nouns usually still take the definite article.

So Greek says, literally:

• the phone my
• το τηλέφωνό μου

This is completely normal Greek structure.

English often says just my phone, but Greek usually prefers:

• το βιβλίο μου = my book
• το σπίτι μου = my house
• το τηλέφωνό μου = my phone

So the article is not extra or strange; it is the standard pattern.

Because Greek possessive words like μου, σου, του, της, μας, σας, τους usually come after the noun.

So:

• το τηλέφωνό μου = my phone
• το σπίτι μου = my house

This is one of the big differences from English. English puts my before the noun, but Greek often puts μου after it.

This happens because μου is a weak little word, called an enclitic, and Greek spelling adds an extra accent in certain cases to preserve the correct stress pattern.

The base noun is:

• τηλέφωνο

But when you add μου, it becomes:

• τηλέφωνό μου

You will see the same thing in other phrases:

• ο δάσκαλός μου = my teacher
• ο άνθρωπός μου = my person / my partner
• το όνομά μου = my name

So this is a normal spelling rule, not a change of meaning.

Because πάω σπίτι is an idiomatic Greek way to say go home, just like English says go home without to the.

So:

• πάω σπίτι = I go home
• ξαναπάω σπίτι = I go back home

If you say πάω στο σπίτι, that means more literally I go to the house / to the home, with more emphasis on the physical location.

So in your sentence, σπίτι without στο is the natural choice for home as a destination.