Hun siger, at det der hul er for stort til en lille krog.

Det der hul is a common way to say that hole in Danish, often with a slightly pointing or emphatic feel, like that hole there in English.

• det matches the gender of hul because hul is neuter: et hul
• der adds the demonstrative sense: that one

You can also say det hul in some contexts, but det der hul is very common in everyday Danish when you are clearly pointing something out.

Not exactly, even though it is related historically.

In this sentence, der is part of the demonstrative expression det der. You usually understand det der hul as one unit meaning that hole.

Depending on stress and context, it can feel like:

• that hole
• that hole there

So it is not mainly functioning as a location word here.

Because after demonstratives like den der, det der, den her, and det her, Danish normally uses the noun in the indefinite form, not the definite form.

So you get:

• det der hul
• den her bog

not usually:

• det der hullet
• den her bogen

The demonstrative already makes the noun definite enough in meaning.

At introduces a subordinate clause, like English that in She says that...

So:

• Hun siger, at... = She says that...

In English, that is often omitted, but in Danish at is very normal and often preferred.

Yes. At introduces a subordinate clause, and Danish subordinate clauses follow their own word-order rules.

Here the basic order is:

• det der hul = subject
• er = verb

A useful thing to notice is where adverbs go. For example:

• Hun siger, at det der hul ikke er for stort.

In a subordinate clause, ikke typically comes before the finite verb.

Because hul is a neuter noun: et hul.

When an adjective is used after er and describes a neuter singular noun, it usually takes -t:

• et hul er stort
• hullet er stort

If the noun were a common-gender noun (en-word), you would use stor instead:

• en krog er stor

So stort agrees with hul.

Because in for stort, for is an adverb meaning too or excessively.

This is a very common Danish pattern:

• for stor = too big
• for dyr = too expensive
• for hurtigt = too fast

So er for stort means is too big.

After for + adjective in Danish, you often use til to express what something is too big, too small, too heavy, etc. for.

So:

• for stort til en lille krog = too big for a small hook

This is just the normal Danish pattern. English uses for there, but Danish uses til.

Because krog is a common-gender noun, an en-word:

• en krog

So the article must be en, not et.

Also, lille is a special adjective. In the singular, it stays lille for both common and neuter gender:

• en lille krog
• et lille hul

So the difference is in the article, not in lille.

You know from the dictionary form: et hul.

In Danish, noun gender has to be learned with the noun. Once you know it is et hul, the rest follows:

• det hul
• det der hul
• hullet
• stort

They all reflect the fact that hul is neuter.

Yes. Den der and det der are very common in everyday spoken Danish.

They are often used when speakers point something out, refer back to something visible, or add emphasis. So a learner will hear this kind of phrasing a lot in conversation.

In more neutral or formal styles, speakers may sometimes choose simpler phrasing, but det der hul is completely normal Danish.