Βάζω τα βρόμικα πανιά σε μια λεκάνη με νερό και σαπούνι.

Because Greek often drops subject pronouns when they are already clear from the verb ending.

• βάζω = I put / I am putting
• The ending -ω already tells you the subject is I

You can add εγώ if you want emphasis:

• Εγώ βάζω... = I am the one putting...

But in a normal sentence, leaving it out is completely natural.

Βάζω is the present tense.

Depending on context, it can mean:

• I put
• I am putting
• I usually put

Greek present tense is often broader than English. In this sentence, it most naturally means I am putting or I put as a general action.

These three words match each other:

• τα = the for neuter plural
• βρόμικα = dirty, also neuter plural
• πανιά = cloths/rags, neuter plural

So the adjective agrees with the noun in gender, number, and case.

A useful detail: βρόμικα can look a bit like an adverb to learners, but here it is clearly an adjective because it is describing πανιά.

Πανιά is the plural of πανί.

In this sentence, it most likely means:

• cloths
• rags
• washing cloths
• possibly pieces of fabric

It does not usually mean clothes in general. For clothes, Greek normally uses ρούχα.

Λεκάνη usually means a basin, washbasin, bowl, or tub-like container, depending on context.

In this sentence, it sounds like:

• a basin used for washing things by hand

So it is not necessarily a fixed sink. It is more like a container you put water and soap in.

Σε is a very common Greek preposition and can mean:

• in
• into
• to
• at

The exact meaning depends on the context.

With a verb like βάζω (put), σε usually means into or in:

• βάζω ... σε μια λεκάνη = I put ... into/in a basin

Greek does not usually make a sharp distinction between in and into here the way English sometimes does.

Because μια λεκάνη means a basin, not the basin.

• σε μια λεκάνη = in/into a basin
• στη λεκάνη = in/into the basin

Also:

• στη is a contraction of σε + τη
• But σε + μια does not contract

So:

• σε μια λεκάνη is correct
• στη λεκάνη would mean something more specific

Because Greek often leaves out the article with mass nouns or when speaking in a general way.

So:

• με νερό και σαπούνι = with water and soap

This sounds natural and general.

If you wanted to refer to specific water and specific soap already known in the conversation, you could say:

• με το νερό και το σαπούνι

But in this sentence, the article is not needed.

A learner might notice that several words are in the accusative.

• τα βρόμικα πανιά = direct object of βάζω
• σε μια λεκάνη = after the preposition σε
• με νερό και σαπούνι = after the preposition με

In Modern Greek, common prepositions like σε and με normally take the accusative.

A small extra point: for many neuter nouns, the nominative and accusative forms are the same, so the form may not look different.

Most naturally, it describes the basin:

• a basin with water and soap

So the structure is basically:

• σε μια λεκάνη [με νερό και σαπούνι]

That said, in real life the meaning is very close either way, because putting something into a basin containing water and soap also implies the washing setup.

Yes. Greek word order is more flexible than English word order.

The sentence as given is neutral and natural:

• Βάζω τα βρόμικα πανιά σε μια λεκάνη με νερό και σαπούνι.

But Greek can move things around for emphasis. For example:

• Τα βρόμικα πανιά τα βάζω σε μια λεκάνη με νερό και σαπούνι.

This puts more emphasis on the dirty cloths.

Even when the order changes, the endings and articles help show what each word is doing.

A rough pronunciation guide is:

VA-zo ta VRO-mi-ka pa-NYA se mia le-KA-ni me ne-RO ke sa-PO-ni

A few helpful notes:

• βάζω → stress on βά
• βρόμικα → stress on βρό
• πανιά → the νι sounds like ny in canyon
• λεκάνη → stress on κά
• νερό → stress on the last syllable
• σαπούνι → stress on πού
• και is often pronounced more like ke in normal speech

So πανιά is not pronounced like separate ni-a, but more like nya.