Njezin brat je student kemije i svaki dan ide na fakultet biciklom.

Njezin means her (possessive: belonging to a female person).

• ona = she (subject pronoun)

  • Ona je studentica. = She is a (female) student.

• njezin (also written njen in colloquial speech) = her

  • Njezin brat = Her brother

• njegov = his

  • Njegov brat = His brother

So njezin brat literally means her brother (the brother that belongs to her).

The form of njezin has to agree in gender, number and case with the noun it describes.

• brat = brother → masculine singular, nominative
• The correct matching form is njezin (masculine singular nominative).

Compare:

• njezin brat = her brother (masculine)
• njezina sestra = her sister (feminine)
• njezino dijete = her child (neuter)

So you choose njezin / njezina / njezino based on the noun, not based on the owner.

Brat is in the nominative case, because it is the subject of the sentence (the one doing the action).

• Njezin brat (who? what?) = subject → nominative → brat

Brata is another case (accusative or genitive) and would be used when brat is an object, for example:

• Vidim njegova brata. = I see his brother. (accusative)
• Nemam brata. = I don’t have a brother. (genitive)

Here we are saying Her brother is a chemistry student…, so brat must be nominative.

Je is the 3rd person singular present form of biti (to be).

• je = is

So:

• Njezin brat je student kemije. = Her brother is a chemistry student.

In spoken, informal Croatian, people often drop je here:

• Njezin brat student kemije.

This is understandable and common in speech, but in standard written Croatian, you normally keep je.

Kemije is the genitive singular of kemija (chemistry).

After words like student, Croatian often uses the genitive to say “student of X”:

• student kemije = student of chemistry
• student medicine = student of medicine
• student prava = law student (literally: student of law)

You can say kemijski student, but that would sound more like a chemical student (as if the student is chemical), which is odd. The natural way is student kemije.

Croatian has no articles like English a / an / the.

• je student kemije can mean is a chemistry student or is the chemistry student, depending on context.
• na fakultet can mean to university, to the faculty, etc., again depending on context.

Specificity (a/the) is usually understood from context, word order, or additional words, not from articles.

Fakultet is usually:

• a faculty or college, i.e. one part of a university (Faculty of Science, Faculty of Law, etc.),
  and in everyday speech it often means
• university in general, especially “where I study”.

Other terms:

• sveučilište = university (the whole institution)
• škola = school (primary/secondary school most commonly)

In real usage, a student will very often say:

• Idem na fakultet. ≈ I’m going to uni / to (my) college.

Both na and u can mean to / in, but usage is partly traditional and partly about how speakers conceptualize the place.

For universities and faculties, people typically say:

• na fakultet (motion, to the faculty/uni)
• na fakultetu (location, at the faculty/uni)

So:

• ide na fakultet = he goes to university (accusative after na for motion)
• je na fakultetu = he is at university (locative after na for location)

Using u fakultet would sound wrong in this context. With školu (school), you usually say u školu / u školi.

The case changes depending on motion vs. location:

• na + accusative → motion towards/onto something (where to?)

  • ide na fakultet = goes to university

• na + locative → static location (where?)

  • je na fakultetu = is at university

In your sentence there is movement (he goes there every day), so it must be na fakultet (accusative).

Svaki dan means every day.

• dan = day, masculine singular (nominative)
• svaki is the masculine singular form of svaki (every), agreeing with dan.

Svaki declines like an adjective:

• svaki dan = every day (masculine)
• svaka noć = every night (feminine)
• svako jutro = every morning (neuter)

In the sentence, svaki dan is an adverbial phrase of time: every day (he goes).

Ide is the 3rd person singular of ići = to go.

• on ide = he goes / he is going

Other verbs:

• hodati = to walk (emphasizes the way of moving on foot)
• voziti (se) = to drive / ride (a vehicle), to travel (by some means)

In practice, for routine movement to a place, Croatians usually use ići:

• Svaki dan ide na fakultet biciklom.
  = Every day he goes to university by bike.

You could say vozi bicikl na fakultet, but that focuses more on riding the bike as an activity. Ide na fakultet biciklom focuses on him going to university, and just mentions that the means is a bike.

Biciklom is the instrumental singular of bicikl (bicycle).

The instrumental case is used here to express the means by which something is done:

• biciklom = by bike
• autobusom = by bus
• autom = by car
• vlak (nom.) → vlakom (instr.) = by train

So:

• ide na fakultet biciklom = he goes to university by bike.

You can also say:

• ide na fakultet na biciklu = he goes to university on the bicycle.

This is also correct, but biciklom is the more usual, compact way to say by bike.

Croatian word order is flexible, and all of these are grammatical:

• Njezin brat je student kemije i svaki dan ide na fakultet biciklom.
• Njezin brat je student kemije i ide svaki dan na fakultet biciklom.
• Svaki dan njezin brat ide na fakultet biciklom.
• Njezin brat svaki dan ide biciklom na fakultet.

The core meaning (her brother is a chemistry student and goes to university by bike every day) stays the same.
Changes in order mainly affect rhythm and emphasis:

• Starting with Svaki dan… stresses the frequency (every day).
• Moving biciklom earlier can emphasize the means of transport.

For a learner, the original sentence is a very neutral, natural order.