Den samme regel gælder også her.

Because regel is a common-gender noun in Danish, so the demonstrative/article form used here is den.

• en regel = a rule
• reglen = the rule
• den samme regel = the same rule

In Danish, den/det/de is often used before an adjective when the noun is definite in meaning:

• den samme regel = the same rule
• det store hus = the big house
• de nye bøger = the new books

So den samme regel is a normal definite noun phrase meaning the same rule.

Both can exist, but they do not mean exactly the same thing in all contexts.

• samme regel can sometimes mean same rule in a more general or less explicitly definite way.
• den samme regel is the standard way to say the same rule when referring to a specific rule already known from the context.

In this sentence, Danish strongly prefers den samme regel because it refers to a specific rule that also applies here.

Because after den samme, the noun usually stays in its indefinite form.

This is a very common Danish pattern:

• den samme regel
  not den samme reglen

Compare:

• den gamle mand = the old man
• det røde æble = the red apple
• de små børn = the small children

So even though the whole phrase is definite in meaning, the noun itself is not marked with the definite ending. The definiteness is already shown by den.

Samme means same.

A useful thing to know is that samme does not change form for gender or number the way many other adjectives do. So you get:

• den samme regel
• det samme problem
• de samme regler

That makes it easier to use than many Danish adjectives.

Because regel is a common-gender noun, and common-gender nouns take den.

Danish has two grammatical genders:

• common gender: usually learned with en
• neuter gender: usually learned with et

Since it is:

• en regel

it becomes:

• den samme regel

If the noun were neuter, you would use det:

• et problem
• det samme problem

Gælder is the present tense of at gælde, which often means:

• to apply
• to be valid
• to concern
• to hold true

In this sentence, the most natural meaning is applies:

• Den samme regel gælder også her.
• The same rule also applies here.

So gælder is a very useful verb when talking about rules, laws, conditions, and exceptions.

Because Danish is a V2 language in main clauses. That means the finite verb normally comes in the second position.

In this sentence:

• Den samme regel = first element
• gælder = second-position verb
• også her = the rest

This is standard Danish word order.

You can see the same pattern in other examples:

• Jeg kommer i morgen.
• Hun arbejder her.
• Den samme regel gælder også her.

If you move another element to the front, the verb still stays second:

• Her gælder den samme regel også.

Because også usually comes before the word or phrase it is closely connected to, and here it naturally modifies her or the whole idea of here too / also here.

So:

• også her = also here / here too

This is very natural Danish.

A few possible word orders exist, but they can sound slightly different in emphasis:

• Den samme regel gælder også her. = neutral, very natural
• Den samme regel gælder her også. = also possible, with a slightly different rhythm or emphasis

For a learner, også her is an excellent standard pattern to remember.

Yes, that is possible.

Both of these can work:

• Den samme regel gælder også her.
• Den samme regel gælder her også.

The difference is mostly one of emphasis and rhythm.

• også her often highlights here too
• her også can sound a bit more conversational or place the also slightly later

The version you were given is very standard and probably the safest one to copy.

Yes, depending on context.

Literally, her means here, but in many real sentences it can be understood more broadly as:

• in this place
• in this context
• in this case

So Den samme regel gælder også her could mean:

• the same rule applies in this place too
• the same rule applies in this situation too

The exact interpretation depends on the surrounding context.

If you wanted to say The same rules also apply here, you would say:

• De samme regler gælder også her.

Notice the changes:

• den → de
• regel → regler
• samme stays samme
• gælder stays gælder

So:

• Den samme regel gælder også her. = singular
• De samme regler gælder også her. = plural

Not quite.

For the same, Danish usually uses samme:

• den samme regel = the same rule

Ens more often means identical / alike / similar in appearance or type, not necessarily the exact same one.

For example:

• De har ens jakker. = They have identical/similar jackets.
• De har de samme jakker. = They have the same jackets.

So in your sentence, samme is definitely the right choice.

A rough guide is something like GEL-er, but the real Danish pronunciation is softer and more reduced than that.

A few points:

• æ sounds somewhat like the vowel in English bed, though not exactly the same.
• The d in gælder is often very soft, not a strong English d.
• The second syllable is usually weak.

If you want a learner-friendly approximation, you can think:

• gælder ≈ GEL-uh

But it is best to hear it from native audio, because Danish pronunciation is often much less clearly pronounced than the spelling suggests.

It works in both formal and everyday Danish.

It is a very natural sentence for:

• explanations
• instructions
• regulations
• discussions
• everyday conversation

For example, a teacher, colleague, official, or friend could all say it.

So this is a useful sentence pattern to learn because it sounds normal in many situations.