Die eienaar gee die kilometerlesing vir die kwotasie.

Yes. In both places, die means the.

Afrikaans uses die as the definite article for nouns very broadly, so you do not have to learn different forms for masculine, feminine, or neuter nouns the way you do in some other languages.

In this sentence:

• die eienaar = the owner
• die kilometerlesing = the mileage/odometer reading

Also, die is not pronounced like English die. It is pronounced roughly like dee.

Mostly because of word order.

In a normal Afrikaans main clause, the usual order is:

Subject + Verb + Object

So here:

• Die eienaar = subject
• gee = verb
• die kilometerlesing = object

Afrikaans nouns and articles do not change form to show subject vs object the way English pronouns do with he/him, she/her, etc. That means word order is especially important.

Because Afrikaans verbs usually do not change form for different persons in the present tense.

So you get:

• ek gee = I give
• jy gee = you give
• hy gee = he gives
• ons gee = we give
• hulle gee = they give

That is much simpler than English, where you have give but also gives.

Here, vir means for.

So vir die kwotasie means for the quotation/estimate or for the quote.

In this sentence, it shows the purpose or intended use of the mileage reading: the owner gives the reading for the quote.

Because Afrikaans normally writes compound nouns as one word.

So:

• kilometer = kilometer
• lesing = reading

Together:

• kilometerlesing = kilometer reading / mileage reading / odometer reading

English often uses separate words where Afrikaans prefers one combined word. This is very common in Afrikaans.

Kwotasie usually means a quote, quotation, or estimate in a business or service context.

In this sentence, it most likely means something like a repair quote or service estimate.

It does not usually mean a quotation of someone’s words. For that kind of quotation, Afrikaans would more likely use another word such as aanhaling.

You would usually say:

Die eienaar het die kilometerlesing vir die kwotasie gegee.

This uses the common Afrikaans past construction:

• het
  • past participle

So:

• gee = give
• gegee = given

Afrikaans often uses this perfect-style past tense where English might simply use gave.

It can mean either, depending on context.

Afrikaans often uses the simple present where English might use:

• gives
• is giving
• does give
• provides

So Die eienaar gee die kilometerlesing vir die kwotasie could mean:

• The owner gives the mileage reading for the quote
• The owner is giving the mileage reading for the quote
• The owner provides the mileage reading for the quote

Usually the situation makes the meaning clear.