Kennarinn les ritgerðina mína vandlega.

Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word.

• kennari = teacher
• kennarinn = the teacher
• ritgerð = essay
• ritgerðina = the essay (here in the accusative)

A separate article exists in Icelandic, but in ordinary sentences like this, the suffixed article is the normal choice.

In standard Icelandic, when a possessive pronoun comes after the noun, the noun is usually also marked as definite.

So Icelandic commonly says:

• bókin mín = my book
• húsið mitt = my house
• ritgerðina mína = my essay (accusative)

So even though English does not say the my essay, Icelandic normally uses the suffixed definite article together with a following possessive.

Kennarinn is nominative singular.

It is nominative because it is the subject of the sentence — the one doing the action of reading.

The base noun is kennari = teacher, and -inn makes it definite: the teacher.

Because it is the direct object of les.

The verb lesa normally takes its direct object in the accusative case, so ritgerð changes to ritgerðina here.

A useful contrast is:

• ritgerðin = the essay as a subject
• ritgerðina = the essay as a direct object

So the ending helps show what role the noun has in the sentence.

Because Icelandic possessives must agree with the noun they describe in gender, number, and case.

The noun ritgerð is:

• feminine
• singular
• accusative in this sentence

So the correct form is mína.

Compare:

• minn kennari / kennarinn minn = my teacher (masculine)
• mitt hús / húsið mitt = my house (neuter)
• ritgerðina mína = my essay (feminine accusative singular)

Because that is the most common and neutral pattern in Icelandic.

A possessive pronoun often comes after the noun:

• bókin mín
• vinur minn
• ritgerðina mína

Putting the possessive before the noun is possible, but it is usually more emphatic, contrastive, or stylistically marked:

• mín ritgerð = my essay with extra emphasis on my

So in an ordinary sentence like this, ritgerðina mína is the natural choice.

Les is the present tense, third person singular form of the verb lesa = to read.

So:

• ég les = I read / I am reading
• hann/hún les = he/she reads / is reading

In this sentence, the subject is singular (kennarinn), so the verb is les.

Also, Icelandic often uses the simple present where English might use either reads or is reading, depending on context.

Vandlega is an adverb meaning carefully.

It tells you how the teacher reads the essay.

It is not describing a noun, so it does not change for gender, number, or case. It modifies the verb les.

So:

• kennarinn = who
• les = does what
• ritgerðina mína = what is being read
• vandlega = how it is being read

This sentence uses a very normal, neutral order:

subject + verb + object + adverb

• Kennarinn = subject
• les = verb
• ritgerðina mína = object
• vandlega = adverb

Icelandic does allow word order changes for emphasis, but the finite verb usually stays in the second position in a main clause.

For example, you could also say:

Ritgerðina mína les kennarinn vandlega.

That puts more focus on my essay, but the verb les still stays in second position.