Gyúrjuk az agyagot.

Because Hungarian usually builds the subject into the verb.

In gyúrjuk, the ending -juk already tells you the subject is we. So Hungarian often leaves out the pronoun mi (we) unless it is being emphasized.

• Gyúrjuk az agyagot. = We knead the clay.
• Mi gyúrjuk az agyagot. = We are the ones kneading the clay. / It’s us who knead the clay.

So the hidden we is inside the verb form.

Because the sentence has a definite direct object: az agyagot = the clay.

Hungarian has two main kinds of verb conjugation in forms like this:

• indefinite conjugation: used when there is no definite object
• definite conjugation: used when the object is definite

Here, az agyagot is definite because of az (the), so the verb takes the definite form:

• gyúrunk = we knead / we are kneading something
• gyúrjuk = we knead it / we are kneading the clay

This is a very important feature of Hungarian grammar.

Gyúrjuk can be analyzed like this:

• gyúr- = the verb stem, from gyúrni (to knead)
• -juk = a we ending used here in the definite conjugation

So gyúrjuk means something like:

• we knead it
• or, with the full object present, we knead the clay

Hungarian often packs a lot of grammatical information into the verb ending.

The dictionary form is gyúrni, which means to knead.

In Hungarian, dictionary forms of verbs usually end in -ni, like:

• beszélni = to speak
• enni = to eat
• gyúrni = to knead

So if you want to look up gyúrjuk, you would look for gyúrni.

Because agyagot is the direct object form of agyag (clay).

Hungarian marks direct objects with the accusative case, usually with -t. In this word, that appears as -ot:

• agyag = clay
• agyagot = clay, as a direct object

So:

• az agyag = the clay
• az agyagot = the clay, as the thing being kneaded

English usually does not change the noun here, but Hungarian does.

Because Hungarian often inserts a linking vowel before certain endings to make the word easier to pronounce.

Here the accusative ending is basically -t, but with this noun it appears as -ot:

• agyag
  • -t → agyagot

This is normal. Many Hungarian nouns do this.

Also, the vowel o fits Hungarian vowel harmony, because agyag contains back vowels (a, a), so a back-vowel form like -ot is used rather than something like -et.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

Since agyagot begins with a vowel sound, the correct form is:

• az agyagot

Compare:

• a könyvet = the book
• az almát = the apple

So az is used simply because the next word starts with a vowel.

No, Hungarian word order is quite flexible, but different orders can change the emphasis.

Gyúrjuk az agyagot is a natural neutral sentence.

You could also say:

• Az agyagot gyúrjuk.

That usually puts more emphasis or focus on the clay, as if contrasting it with something else:

• It’s the clay that we’re kneading.

So the words can move, but the choice of order affects what sounds emphasized, topical, or contrastive.

Yes, it can.

This form gyúrjuk can be ambiguous because it can match both:

• a present indicative form: we knead the clay
• a 1st person plural imperative/subjunctive form: let’s knead the clay

Usually the context tells you which meaning is intended.

So if you see this sentence by itself, both are grammatically possible. In real usage, tone, surrounding sentences, or situation would usually make the meaning clear.

A rough English-friendly guide would be:

• gyúrjuk ≈ dyoor-yook
• az agyagot ≈ awz aw-dyaw-got

A few key points:

• gy is a special Hungarian sound, roughly like a soft dy
• ú is a long vowel, like oo in food, but held longer
• j is pronounced like English y
• s in Hungarian is always like English sh, but there is no s here
• a in Hungarian is not exactly like English a; it is more open and rounded

A more accurate pronunciation in IPA is:

• Gyúrjuk az agyagot = [ˈɟuːrjuk ɒz ˈɒɟɒɡot]

Not always, but here it makes the object definite: the clay.

Compare:

• Gyúrunk agyagot. = We knead clay. / We are kneading some clay.
• Gyúrjuk az agyagot. = We knead the clay.

So the article is not required in every sentence, but if you want to say the clay, then yes, you use the definite article.

Also notice that changing the object from indefinite to definite changes the verb form too:

• gyúrunk
  • agyagot
• gyúrjuk
  • az agyagot

That connection between the object and the verb is a central part of Hungarian grammar.