Die passasier gaan die band na en pak die spaarwiel.

Neither in the usual sense. Here gaan ... na is the separable verb nagaan, which means check, inspect, or go over.

So in this sentence, gaan is part of one verb, and na is the other part of that same verb.

Compare:

• Die passasier gaan die band na. = The passenger checks the tire.
• Die passasier gaan die spaarwiel pak. = The passenger is going to pack/load the spare wheel.

In the second example, gaan really is the future-style helper verb. In your sentence, it is not.

Because nagaan is a separable verb.

In Afrikaans main clauses, the first part of a separable verb appears in the normal verb position, and the second part moves to the end of the clause:

• nagaan → gaan ... na
• oopmaak → maak ... oop

So:

• Die passasier gaan die band na.

This is very normal Afrikaans word order.

When the verb is not split, it appears as one word again, for example:

• om die band na te gaan = to check the tire
• hy het die band nagegaan = he checked the tire

That is the usual pattern for a separable verb in a main clause:

finite verb + object + particle

So:

• gaan = first part of the verb
• die band = object
• na = separated particle

This means gaan die band na is correct.

If you said gaan na die band, then na would sound like the ordinary preposition to/toward, and the meaning would change to something more like go to the tire, not check the tire.

Because die is the Afrikaans definite article, meaning the.

Each noun phrase normally has its own article:

• die passasier = the passenger
• die band = the tire
• die spaarwiel = the spare wheel

Afrikaans does not change the for gender, so you do not have to learn separate forms like in some other languages. Die is used very widely for the.

Yes. Band can mean different things depending on context, but in car-related contexts it commonly means tire/tyre.

Because the sentence also has spaarwiel (spare wheel), the vehicle meaning is clearly intended here.

So although an English speaker may first think of band as a music group or strip of material, here it means tire.

Because Afrikaans verbs usually do not change form in the present tense depending on the subject.

Compare English:

• I pack
• he packs

In Afrikaans, both stay the same:

• ek pak
• hy pak
• die passasier pak

So pak is correct with die passasier. There is no extra -s ending.

Pak is a flexible Afrikaans verb. Depending on context, it can mean things like pack, load, grab, take, or put.

So the exact English translation depends on the situation described in your material. In this sentence, use the meaning already given to you, but it is useful to know that pak is broader than just one English verb.

That is very common in Afrikaans: one everyday verb may cover several English verbs.

Because Afrikaans usually writes compound nouns as a single word.

So:

• spaar = spare
• wiel = wheel
• spaarwiel = spare wheel

This is extremely common in Afrikaans. The last part is usually the main noun, and the first part describes it.

You will see the same pattern in many other words too.

Because the subject is understood to be the same for both verbs.

So:

• Die passasier gaan die band na en pak die spaarwiel.

means the same subject does both actions:

1. checks the tire
2. packs/loads/takes the spare wheel

Afrikaans, like English, often leaves out the repeated subject in this kind of coordinated sentence. The fully expanded version would be possible but unnecessarily repetitive:

• Die passasier gaan die band na en die passasier pak die spaarwiel.

The shorter version is the natural one.