Ανοίγω τη ζύμη με τον πλάστη και μετά τη βάζω στο ταψί.

Yes. Ανοίγω very often means open, but in cooking it also has the extended meaning to spread out / roll out dough.

So with ζύμη (dough), ανοίγω τη ζύμη means I roll out the dough.

This is a very common cooking use:

• Ανοίγω τη ζύμη = I roll out the dough
• Ανοίγω φύλλο = I roll out pastry sheet / phyllo

So this is one of those cases where the basic idea of opening/spreading becomes a specialized cooking meaning.

Because ζύμη is the direct object of the verb.

• η ζύμη = the dough as the subject form
• τη(ν) ζύμη = the dough as the object form

Here, the speaker is doing something to the dough, so Greek uses the accusative:

• Ανοίγω τη ζύμη = I roll out the dough

Compare:

• Η ζύμη είναι έτοιμη. = The dough is ready.
  (η ζύμη = subject)
• Ανοίγω τη ζύμη. = I roll out the dough.
  (τη ζύμη = object)

Both are connected. The full accusative feminine singular article/pronoun is την, but in everyday speech and writing it is very often shortened to τη before a consonant.

So:

• την ζύμη and τη ζύμη both mean the same thing
• τη ζύμη is very common and natural

The same happens later in the sentence:

• τη βάζω = I put it

You will often see the full form την in more careful spelling, but τη is extremely common in modern Greek.

Ο πλάστης means rolling pin.

It is a masculine noun:

• nominative: ο πλάστης
• accusative: τον πλάστη

After με here, Greek uses the accusative form, so:

• με τον πλάστη = with the rolling pin

So the sentence uses:

• τον πλάστη because that is the correct form in this structure

Here με means with, showing the tool/instrument used.

So:

• με τον πλάστη = with the rolling pin

In other contexts, με can also mean:

• with someone
• by means of something
• sometimes part of expressions

But in this sentence it is simply the instrument:

• I roll out the dough with the rolling pin.

That τη is not the article the. It is a pronoun meaning it, referring back to τη ζύμη.

So:

• τη ζύμη = the dough
• τη βάζω = I put it

Greek often uses these short object pronouns before the verb:

• τον = him / it
• τη(ν) = her / it
• το = it

Because ζύμη is feminine, the pronoun is τη.

Because in Greek, weak object pronouns normally come before the finite verb.

So Greek says:

• τη βάζω = literally it I-put

This is normal Greek word order for object pronouns.

Compare:

• Βάζω τη ζύμη στο ταψί. = I put the dough in the tray.
• Τη βάζω στο ταψί. = I put it in the tray.

English puts it after the verb, but Greek usually puts τη before the verb.

Because Greek usually does not need an explicit subject pronoun if the verb ending already shows who the subject is.

• Ανοίγω = I open / I roll out
• βάζω = I put

The -ω ending tells you the subject is I.

So εγώ is usually omitted unless you want emphasis or contrast:

• Εγώ ανοίγω τη ζύμη, όχι εσύ. = I roll out the dough, not you.

In a normal sentence, leaving out εγώ is the most natural choice.

Μετά means after / afterwards / then, depending on context.

In this sentence:

• και μετά = and then

It links the two actions in sequence:

1. Ανοίγω τη ζύμη
2. μετά τη βάζω στο ταψί

So it shows the order clearly: first one action, then the next.

Because στο is the contracted form of σε + το.

• σε = in / into / on / at
• το = the
• στο = σε το

So:

• στο ταψί = in/into the baking tray

This contraction is standard and very common:

• στο σπίτι = in the house / at home
• στο τραπέζι = on the table
• στο ταψί = in the tray

Το ταψί means baking tray / pan.

It is a neuter noun:

• nominative: το ταψί
• accusative: το ταψί

Many neuter nouns have the same form in nominative and accusative, which is why it stays το ταψί after στο.

So:

• στο ταψί = into the baking tray

Greek often uses the present tense for:

• instructions
• recipes
• demonstrations
• describing a sequence of actions

So Ανοίγω... και μετά βάζω... can sound like:

• I roll out... and then I put... or, in recipe-style English,
• Roll out... and then put...

This use of the present is very natural in Greek when explaining a process step by step.

Yes, Greek word order is fairly flexible, although some versions sound more natural than others.

The given sentence:

• Ανοίγω τη ζύμη με τον πλάστη και μετά τη βάζω στο ταψί.

A slightly different but still natural version:

• Ανοίγω τη ζύμη με τον πλάστη και μετά βάζω τη ζύμη στο ταψί.

That version repeats the noun instead of using the pronoun, but Greek usually prefers the pronoun once the object is already known:

• τη βάζω = more natural than repeating τη ζύμη

So the original sentence sounds very natural and efficient.

They look the same, but they do different jobs.

In:

• τη ζύμη

  τη is the definite article = the

In:

• τη βάζω

  τη is an object pronoun = it / her

So:

• τη ζύμη = the dough
• τη βάζω = I put it

This is very common in Greek, and learners often notice it early because the forms are identical.