Because Afrikaans uses the definite article before each definite noun phrase.
So you need die in both places. Afrikaans does not reuse one article for the whole sentence.
In Afrikaans, adjectives do not always change form before a noun. fyn is one of the adjectives that normally stays the same here, so die fyn sand is correct.
A useful comparison:
Afrikaans adjective endings are less extensive than in languages like Dutch or German, so it is often best to learn them from examples.
op is the normal preposition for on in this kind of sentence, and op die strand is the usual way to say on the beach.
Related phrases can differ slightly:
So op die strand is the straightforward choice here.
Yes, in this simple main clause it is very similar:
So the pattern is subject + verb + location, just like English.
However, Afrikaans has a stronger verb-second rule than English. If another part of the sentence comes first, the verb still stays in second position. So this sentence is simple, but it also fits a broader Afrikaans pattern.