Learn Hardcore Hungarian: A diák meg akarja mutatni a képet a tanárnak. - The student wants to show the picture to the teacher.

Hungarian marks whether a verb has a definite object. Here, the object of the infinitive mutatni is definite (a képet), so the modal verb takes the definite 3rd‑person ending: akarja. If the object were indefinite or not specified, you would use the indefinite form akar.

Does the definite object of mutatni really control the conjugation of akar?

Yes. In verb + infinitive constructions, the definiteness of the infinitive’s object “raises” to the finite modal, so the modal shows definite conjugation if the object is definite. Compare:

Definite object: A diák meg akarja mutatni a képet.
Indefinite object: A diák meg akar mutatni egy képet.

Can I say A diák meg akar mutatni a képet a tanárnak?

Not with the definite object a képet. With a definite object you must use definite conjugation on the modal: A diák meg akarja mutatni a képet a tanárnak. The version without -ja is fine only if the object is indefinite: meg akar mutatni egy képet.

Where does the particle meg go with a modal like akar?

Neutral placement is before the finite modal: meg akarja mutatni. Under negation, the particle attaches to the infinitive: Nem akarja megmutatni. If you focus something right before the modal, the particle typically stays with the infinitive: A diák a képet akarja megmutatni (it’s the picture he wants to show). Avoid splitting meg from mutatni with the object.

Why is a képet in the accusative -t, while a tanárnak has -nak?

a képet is the direct object, so it takes the accusative suffix -t.
a tanárnak marks the recipient/indirect object with the dative -nak/‑nek, which corresponds to English “to” (to the teacher). The choice -nak vs -nek follows vowel harmony; tanár has back vowels, so -nak.

Can I switch the order of a képet and a tanárnak?

Yes. Both … meg akarja mutatni a képet a tanárnak and … meg akarja mutatni a tanárnak a képet are fine. Use word order to manage emphasis; put the element you want to highlight closer to the verb or in focus position (immediately before the finite verb: akarja). With pronouns, Hungarian tends to place the pronoun earlier: … meg akarja mutatni neki a képet.

What does meg add to mutatni? Is mutatni without meg wrong?

meg- generally adds a sense of completion/achievement. megmutatni is the idiomatic way to say “to show (so that the other person sees it).” mutatni on its own means “to show” as an activity and is grammatical, but in this context megmutatni is what you normally want.

How do I negate this sentence?

Place nem before the finite verb and keep meg with the infinitive: A diák nem akarja megmutatni a képet a tanárnak. Don’t say nem meg akarja mutatni in this meaning.

How do I ask “What does the student want to show to the teacher?” and “To whom does the student want to show the picture?”

What: Mit akar a diák megmutatni a tanárnak? (Note the indefinite akar because the object is now the unknown mit.)
To whom: Kinek akarja a diák megmutatni a képet? (The picture remains definite, so akarja stays definite.)

Why do we use a and not az (or vice versa) with these nouns?

Hungarian uses a before a consonant sound and az before a vowel sound:

a diák, a képet, a tanárnak (all start with consonants)
but e.g. az alma, az órát (start with vowels).

Can I drop the articles, like “Meg akarja mutatni képet tanárnak”?

No. Hungarian articles are used with specific nouns much more consistently than in English. Keep them: … a képet a tanárnak. If you mean an indefinite referent, use egy: … egy képet egy tanárnak (and then the modal becomes akar, not akarja).

How would the sentence change with plural subject “students”?

Definite object: A diákok meg akarják mutatni a képet a tanárnak. (3PL definite: akarják)
Indefinite object: A diákok meg akarnak mutatni egy képet egy tanárnak. (3PL indefinite: akarnak)

Is mutatni an infinitive? How is it formed?

Yes. The Hungarian infinitive is typically formed with -ni attached to the verb stem: mutat → mutatni, ír → írni, tanul → tanulni. Some verbs are irregular (e.g., megy → menni).

Can I replace a tanárnak with a pronoun?

Yes: A diák meg akarja mutatni neki a képet. You can also emphasize with őneki: … meg akarja mutatni őneki a képet (more contrastive). Use the dative pronoun (neki/őneki), not the accusative (őt), because it’s an indirect object.

How do I strongly emphasize the picture or the recipient?

Put the focused element immediately before the finite verb and keep meg with the infinitive:

Emphasize the picture: A diák a KÉPET akarja megmutatni a tanárnak (nem a videót).
Emphasize the recipient: A diák a TANÁRNAK akarja megmutatni a képet (nem a szülőnek).

What if the person who wants is not the one who shows?

Then you use a hogy‑clause with a finite verb (often in subjunctive): A diák azt akarja, hogy a barátja megmutassa a képet a tanárnak. You can’t use an infinitive if the subject of the lower action is different.