De wachtlijst bepaalt de opvangplek.

Because Dutch normally writes compound nouns as a single word.
Wachtlijst is made from wacht + lijst, literally something like wait-list.

This is very common in Dutch:

• treinstation
• huisdeur
• kinderopvang

Where English often uses two words, Dutch often joins them.

It is also a compound noun: opvang + plek.

• opvang can mean things like care, reception, shelter, or childcare, depending on context
• plek means place, spot, or space

So opvangplek means a place/spot in some kind of care or childcare setting. The exact English wording depends on the context you were given.

Bepalen is the infinitive, meaning to determine or to decide.
In the sentence, the subject is de wachtlijst, which is third-person singular, so Dutch uses the present-tense form bepaalt.

Compare:

• ik bepaal = I determine
• jij bepaalt = you determine
• de wachtlijst bepaalt = the waiting list determines

So the final -t is just normal present-tense agreement.

Because the grammatical subject is de wachtlijst, and that is one list.
Dutch verb agreement follows the subject grammatically, not the number of people inside the group.

So:

• one list → bepaalt
• two lists → bepalen

Even if the list contains many people, the noun wachtlijst itself is singular here.

Both wachtlijst and opvangplek are de-words. In Dutch singular nouns usually take either de or het, and this is something you often have to learn with each noun.

So here:

• de wachtlijst
• de opvangplek

This does not mean they are plural; they are both singular. It just means they belong to the de gender class.

The sentence follows normal main-clause Dutch word order. The finite verb comes in second position.

Here that gives:

• De wachtlijst = subject
• bepaalt = finite verb
• de opvangplek = object

Because the subject comes first, it looks very similar to English: Subject + verb + object.

If another element came first, Dutch would still keep the verb second:

• Morgen bepaalt de wachtlijst de opvangplek.

It can mean either, depending on context.
In this sentence, it means that the waiting list is the thing that decides or determines what the placement will be.

Possible English renderings might be:

• determines
• decides
• sets

The best choice depends on the exact translation/context already shown to the learner.

Not in normal standard Dutch prose. In a full sentence like this, Dutch normally needs the articles with specific singular count nouns.

So the natural form is:

• De wachtlijst bepaalt de opvangplek.

Without the articles, it sounds more like a headline, note, or very telegraphic style.

A rough guide is vakht-lijst.

A few useful points:

• w in Dutch is usually softer than English w
• ch in wacht is the guttural Dutch sound, similar to the sound in Scottish loch for many speakers
• ij in lijst sounds roughly like the vowel in English price, though not exactly

The main stress falls on the first part: WACHT-lijst.