Μετά τη μετακόμιση θέλω να γεμίσω το σπίτι με φυτά και να αδειάζω το μπαλκόνι από τα άδεια κουτιά κάθε βράδυ.

Because μετά meaning after is followed by the accusative in Modern Greek when it introduces a noun phrase. So τη μετακόμιση is accusative.

Here, μετακόμιση is a noun meaning move / relocation, so the phrase literally means after the move.

The full accusative feminine article is την, but the final -ν is often dropped before many consonants in normal Modern Greek spelling and speech. Since μετακόμιση starts with μ, τη μετακόμιση is the usual form.

So:

• την = full form
• τη = shortened form used before many consonants

Greek can express this idea either way. In this sentence, it uses the noun phrase μετά τη μετακόμιση = after the move.

If you wanted a verb-based version, you could say αφού μετακομίσω, meaning after I move. Both are natural; this sentence simply chooses the noun structure.

Modern Greek normally does not use an infinitive the way English does. After verbs like θέλω, Greek uses να + a subjunctive form.

So:

• θέλω να γεμίσω = I want to fill
• θέλω να αδειάζω = I want to empty / be emptying regularly

This is one of the most basic patterns in Greek grammar.

In Greek, when two verbs are linked and both depend on θέλω, it is very normal to repeat να:

θέλω να γεμίσω ... και να αδειάζω ...

That repeated να clearly marks the second verb as part of the same want to structure. English usually does not need to repeat to, but Greek often does repeat να.

This is an aspect difference.

• να γεμίσω is perfective (aorist-style): it presents the action as a whole, completed event.
• να αδειάζω is imperfective: it presents the action as repeated, ongoing, or habitual.

That fits the sentence well:

• fill the house with plants = one overall result after the move
• empty the balcony of the empty boxes every night = repeated habit

So Greek is showing not just what happens, but how the action unfolds in time.

Yes, but the meaning would change.

• να γεμίζω would suggest a repeated or ongoing filling action
• να αδειάσω would suggest one single completed emptying

So:

• να γεμίσω το σπίτι = fill the house up
• να αδειάζω το μπαλκόνι κάθε βράδυ = empty the balcony every night, as a routine

The forms in the sentence were chosen very deliberately.

Because Greek uses the pattern γεμίζω κάτι με κάτι:

• γεμίζω = fill
• το σπίτι = the thing being filled
• με φυτά = with plants

So the structure is: fill + object + with + thing used to fill it

Here με means with, and φυτά is in the accusative plural.

Because Greek often uses the pattern αδειάζω κάτι από κάτι, meaning empty something of something or clear something from something.

So:

• το μπαλκόνι = what is being cleared
• από τα άδεια κουτιά = from the empty boxes

This is different from English wording, but it is a normal Greek structure.

Both σπίτι and μπαλκόνι are neuter singular nouns, so their definite article is το.

Also, in the neuter singular, the nominative and accusative forms are the same. So even though these words are direct objects here, they still look like το σπίτι and το μπαλκόνι.

Άδεια is an adjective meaning empty, and it agrees with κουτιά in gender, number, and case.

Here:

• κουτιά = neuter plural
• so the adjective is also neuter plural: άδεια

That gives:

• τα άδεια κουτιά = the empty boxes

A useful comparison:

• το άδειο κουτί = the empty box
• τα άδεια κουτιά = the empty boxes

Greek often uses simple time expressions like this without a preposition:

• κάθε βράδυ = every night
• κάθε μέρα = every day
• κάθε χρόνο = every year

So κάθε βράδυ works adverbially to show when the repeated action happens.

Because θέλω να... already means I want to..., and that structure naturally points to a desired future action. Greek does not need θα here.

Compare:

• θέλω να γεμίσω το σπίτι = I want to fill the house
• θα γεμίσω το σπίτι = I will fill the house

If you said θα θέλω να..., it would mean I will want to..., which is a different idea.