Vi bruger kikkerten igen, og denne gang ser vi to rådyr mellem træerne.

Because the sentence has two main clauses joined by og:

1. Vi bruger kikkerten igen
2. denne gang ser vi to rådyr mellem træerne

In Danish, each main clause normally needs its own subject. So even though English might sometimes feel more flexible, Danish repeats vi here naturally.

Kikkerten means the binoculars / the telescope / the spyglass, depending on context. The ending -en is the definite article attached to the noun.

So:

• en kikkert = a pair of binoculars / a telescope
• kikkerten = the binoculars / the telescope

Danish usually puts the at the end of the noun, instead of using a separate word like English does.

Because kikkert is a common gender noun in Danish. Common gender nouns usually take:

• en in the indefinite singular
• -en in the definite singular

So:

• en kikkert
• kikkerten

If it were a neuter noun, you would expect et and often -et instead.

Igen means again. In Vi bruger kikkerten igen, it comes after the object kikkerten.

That word order is very natural in Danish. Danish adverbs like igen often come later in the clause, especially after the verb and object.

Compare:

• Vi bruger kikkerten igen. = natural
• Vi igen bruger kikkerten. = not natural in ordinary Danish

Denne gang means this time. It is a time expression placed at the front for emphasis or to set the scene.

Danish often puts time expressions first:

• I dag ser vi...
• Nu går vi...
• Denne gang ser vi...

Putting denne gang first makes the clause sound very natural: This time, we see...

This is because Danish follows the V2 rule in main clauses: the finite verb must come in the second position.

So when denne gang takes the first position, the verb ser must come next:

• Denne gang ser vi to rådyr...

Structure:

• 1st position: denne gang
• 2nd position: ser
• then subject: vi

This is why Danish says:

• Vi ser to rådyr.
• Denne gang ser vi to rådyr.

but not:

• Denne gang vi ser to rådyr. in a normal main clause

Both can mean this, but they are used a bit differently.

• denne gang = slightly more formal or written-style
• den her gang = very common in spoken Danish

So both are possible:

• denne gang
• den her gang

In a textbook or careful written sentence, denne gang is very normal.

Because denne already makes the noun definite. In Danish, when you use a demonstrative like denne (this), you do not also add the suffixed definite article.

So you say:

• denne gang = this time

not:

• denne gangen

This is similar to English not saying this the time.

Because rådyr is one of those Danish nouns whose singular and plural have the same form.

So:

• et rådyr = a roe deer
• to rådyr = two roe deer

This is similar to English words like deer, where singular and plural are also the same.

Because the sentence means two roe deer, not the two roe deer.

After a number like to, Danish normally uses the indefinite plural form:

• to rådyr = two roe deer
• tre træer = three trees

If you wanted to say the two roe deer, you would say:

• de to rådyr

Mellem træerne means between the trees. The definite plural træerne is used because we are talking about a specific set of trees in the scene.

Forms:

• et træ = a tree
• træer = trees
• træerne = the trees

So:

• mellem træer = between trees in a more general sense
• mellem træerne = between the trees you can see or already know about

It comes from the neuter noun et træ.

The forms are:

• et træ = a tree
• træet = the tree
• træer = trees
• træerne = the trees

The ending -ne is a common definite plural ending in Danish.

Here mellem is the right choice because it means between / among in a physical, spatial sense.

• mellem træerne = physically among or between the trees

Blandt can also mean among, but it is often used more for groups, categories, or less exact spatial relationships:

• blandt venner = among friends
• blandt mange muligheder = among many options

For visible objects in space like trees, mellem is very natural.

Yes, in standard Danish punctuation, a comma before og is common when it joins two full clauses with their own verbs and subjects.

Here we have:

• Vi bruger kikkerten igen
• og denne gang ser vi to rådyr mellem træerne

Since both parts are full clauses, the comma is natural and standard.

Yes. You could say:

• Vi bruger kikkerten igen, og vi ser to rådyr mellem træerne.

That is grammatical, but it changes the nuance a little. Denne gang adds the idea of this time and contrasts with an earlier time when maybe something different happened.

So denne gang gives the sentence more context and flow.

It is tricky mainly because of the Danish vowels.

Very roughly:

• rå has a long vowel something like raw but with a more rounded Danish quality
• dyr contains the Danish y, which is not the same as English y

Also, the word is a compound:

• rå
  • dyr

Even if pronunciation is difficult at first, the important grammar point is that rådyr is neuter and keeps the same form in singular and plural.

Yes. Danish en kikkert is grammatically singular, but in many contexts it corresponds to English binoculars, which is plural in form.

So:

• Vi bruger kikkerten igen can naturally mean We use the binoculars again

This is just one of those cases where Danish and English package the idea differently.