Moja šefica kaže da je ovo najteži projekat ove godine.

Because moja has to agree with šefica, which is a feminine singular noun.

• moj = masculine singular
• moja = feminine singular
• moje = neuter singular

So:

• moj šef = my male boss
• moja šefica = my female boss

This agreement depends on the noun, not on whether the speaker is male or female. A man would also say moja šefica if his boss is a woman.

Šefica means female boss or female manager.

It is the feminine form related to šef:

• šef = boss, chief, male boss
• šefica = female boss

In everyday Serbian, using šefica is very normal when referring to a woman in that role.

Kaže is the 3rd person singular present tense form, meaning says.

So:

• ja kažem = I say
• ti kažeš = you say
• on/ona kaže = he/she says

In this sentence, the subject is moja šefica, so the verb must be kaže.

Da introduces a subordinate clause, and here it works like English that:

• Moja šefica kaže da... = My boss says that...

In English, that is often optional:

• My boss says this is the hardest project...

In Serbian, da is normally used in this kind of sentence.

Je is the short form of jeste, from the verb biti = to be.

The inner statement is:

• Ovo je najteži projekat ove godine.
• This is the hardest project this year.

So after kaže da, you still need the verb to be inside that clause.

Also, je is a clitic in Serbian, which means it tends to stand near the beginning of its clause. That is why you get:

• da je ovo...

and not normally:

• da ovo je...

This is a very common question.

In sentences like This is X, Serbian often uses ovo as a general demonstrative pronoun, even if the noun that follows is masculine or feminine:

• Ovo je moj brat.
• Ovo je moja sestra.
• Ovo je najteži projekat...

So ovo here means something like this thing / this here.

By contrast, ovaj is used when directly modifying a masculine noun:

• ovaj projekat = this project

So:

• Ovo je najteži projekat. = This is the hardest project.
• Ovaj projekat je najteži. = This project is the hardest.

Both are possible, but they are structured differently.

Najteži is the superlative form of the adjective težak.

The pattern is:

• težak = hard, difficult, heavy
• teži = harder, more difficult
• najteži = hardest, most difficult

The prefix naj- creates the superlative in Serbian.

So najteži projekat literally means the hardest project.

Because it agrees with projekat, which is masculine singular nominative.

Adjectives in Serbian must agree with the noun they describe in:

• gender
• number
• case

Here:

• projekat = masculine
• singular
• nominative

So the adjective is:

• najteži projekat

If the noun were feminine, the form would change:

• najteža knjiga = the hardest book

If it were neuter:

• najteže pitanje = the hardest question

Projekat is in the nominative singular.

That is the normal form you see in dictionaries, and it is used here because it is the predicate noun after je in an identification/equational sentence:

• Ovo je projekat.
• This is a project.

So in:

• Ovo je najteži projekat...

both ovo and projekat are part of a sentence built around je.

You may also notice that some speakers use or recognize the variant projekt, but projekat is very common and standard.

Because Serbian often uses the genitive for time expressions like this.

• godina = year
• ove godine = this year

Literally, it is something like of this year, but in natural English we usually translate it as this year.

The forms are:

• ova godina = this year, as a subject or noun phrase
• ove godine = this year, in a time expression

So:

• Ova godina je teška. = This year is hard.
• Najteži projekat ove godine = the hardest project this year

Because ove has to match the case of godine.

The noun is godina, but in this phrase it becomes godine because it is in the genitive singular. The adjective/demonstrative must match it, so:

• nominative: ova godina
• genitive: ove godine

This kind of matching happens all the time in Serbian.

There is no separate word for the because Serbian does not have articles like English a/an/the.

So Serbian expresses definiteness through context, word order, or demonstratives such as:

• ovaj = this
• taj = that
• onaj = that over there

Here, najteži projekat can naturally mean the hardest project from context.

Yes, Serbian word order is more flexible than English word order, but the sentence you have is the most neutral and natural version.

Neutral order:

• Moja šefica kaže da je ovo najteži projekat ove godine.

You can move some parts for emphasis, for example:

• Moja šefica kaže da je ovo ove godine najteži projekat.

That can sound slightly more emphatic around ove godine.

But one important thing does not usually change:

• je should stay in its clitic position near the start of the clause

So:

• da je ovo... = natural
• da ovo je... = not the normal standard order

A rough pronunciation guide is:

• Moja ≈ MO-ya
• šefica ≈ SHE-fi-tsa
• kaže ≈ KAH-zheh
• da je ≈ dah yeh
• ovo ≈ OH-vo
• najteži ≈ NAI-teh-zhee
• projekat ≈ pro-YEH-kat
• ove godine ≈ OH-veh GO-dee-neh

A few useful sound notes:

• š = sh as in shoe
• ž = the sound in measure
• j = y as in yes
• c = ts as in cats

So šefica kaže is roughly SHE-fi-tsa KAH-zheh.