De måtte aflyse besøget hos bedstemor, fordi bedstefar blev syg.

It can be either, depending on context.

A tricky detail: because De is the first word of the sentence, it has to be capitalized anyway. So the capital D does not tell you whether it is:

• de = they
• De = formal you

In modern Danish, formal De exists but is much less common than it used to be. So you usually decide from context or from the translation you were given.

Here måtte means had to.

It is the past tense of må, and in this sentence it expresses necessity:

• De må aflyse = they have to cancel / they must cancel
• De måtte aflyse = they had to cancel

English learners often notice that måtte can also mean something like was/were allowed to in some contexts. That is true, but here the reason clause — fordi bedstefar blev syg — makes the meaning clearly had to.

Because måtte is a modal verb, and modal verbs in Danish are followed by the bare infinitive.

So you get:

• måtte aflyse
• not måtte at aflyse

This is similar to English with modal verbs:

• can go
• must leave
• not can to go

Common Danish modal verbs include:

• kan
• skal
• vil
• må
• burde
• kunne
• skulle
• ville
• måtte

Because besøget is the definite singular form: the visit.

Danish usually marks definiteness by adding an ending to the noun:

• et besøg = a visit
• besøget = the visit

Here it is a specific, known visit — the one they were planning to make — so Danish uses the definite form.

Also, besøg is a neuter noun, which is why the indefinite form is et besøg and the definite ending is -et.

Because hos is commonly used with people, especially to mean at someone's place or with someone.

So:

• hos bedstemor = at grandma's place / with grandma

In English, we often say visit grandma or visit grandma's house, but Danish often uses hos in this kind of phrase.

So besøget hos bedstemor is very natural Danish for the visit to grandma or the visit at grandma's place.

Because Danish often uses close family words without a possessive when it is already clear whose relative is meant.

So instead of saying:

• min bedstemor
• min bedstefar

Danish can simply say:

• bedstemor
• bedstefar

This is especially common when talking about one's own family in a natural, everyday way. It works a bit like using a name.

So:

• hos bedstemor
• bedstefar blev syg

sounds very normal.

Using min bedstemor or min bedstefar is also possible, but it can sound more explicit or more contrastive.

Fordi introduces a subordinate clause.

In Danish, the main clause usually follows the V2 rule: the finite verb comes in the second position.

Main clause:

• De måtte aflyse besøget hos bedstemor

After fordi, you get a subordinate clause:

• fordi bedstefar blev syg

In this sentence, the order looks simple: subject + verb. But the important point is that after fordi, Danish is not using main-clause V2 word order.

You can see this more clearly if there is an adverb:

• fordi bedstefar ikke blev syg

Here ikke comes before the finite verb blev, which is typical of a subordinate clause.

Literally, it means became sick.

• blev = past tense of blive = become
• syg = sick / ill

So bedstefar blev syg means:

• grandfather became ill
• more naturally in English: grandfather got sick or grandfather fell ill

This is a very common Danish pattern:

• blive + adjective = become / get + adjective

For example:

• blive træt = get tired
• blive vred = get angry
• blive gammel = grow old

Because the adjective agrees with the subject.

Here the subject is bedstefar, which is:

• singular
• common gender

So the correct form is the basic adjective form:

• bedstefar blev syg

Compare:

• barnet blev sygt = the child got sick
  
  • barnet is neuter singular
• bedsteforældrene blev syge = the grandparents got sick
  
  • plural

So:

• common singular → syg
• neuter singular → sygt
• plural → syge

Because fordi bedstefar blev syg is a subordinate clause, and in standard written Danish it is separated from the main clause with a comma.

So:

• De måtte aflyse besøget hos bedstemor, fordi bedstefar blev syg.

This is normal Danish punctuation.

English punctuation is sometimes a bit looser in similar sentences, so this often stands out to learners.