Bigae quadrigas praetereunt; currus paene colliduntur.

The case endings tell you. Bigae is nominative plural, so it is the subject of praetereunt. Quadrigās is accusative plural, so it is the direct object: the thing being passed.

This is a good example of how Latin depends more on endings than on word order.

Praetereunt is the 3rd person plural present active indicative of praetereō, meaning go past, pass, or overtake. In context, it means that the bigae are passing the quadrigae.

The ending -eunt is a clue that this verb is built from eō (I go), which has some irregular forms.

Currus is a more general word meaning chariot. After mentioning two specific types, Latin can switch to a broader term to refer to them collectively.

English does the same thing all the time: after saying the cars and the trucks, we might then say the vehicles.

Because currus is a 4th-declension noun. Its nominative singular is currus, and its nominative plural is currūs. If macrons are not written, both appear as currus.

You know it is plural here because the verb is plural: colliduntur. If the subject were singular, you would expect colliditur.

Colliduntur is indeed passive in form: it is the 3rd person plural present passive of collidō. Literally, it is something like are dashed together or are struck together.

But Latin often uses a passive-looking form where English prefers an intransitive verb like collide. So here the natural English meaning is simply the chariots almost collide.

Paene means almost or nearly. Here it modifies the verb colliduntur, so it tells you that the collision nearly happens but does not actually happen.

Its position before the verb is normal, but Latin could place it elsewhere if the author wanted a different emphasis.

Yes. Latin word order is flexible because the endings carry so much of the grammatical information. For example, Quadrigās bigae praetereunt would still mean the same basic thing.

That said, the given order is straightforward and easy to follow: subject, object, verb in the first clause, then a short second clause describing what almost happens next.