Min veninde tager en pagaj, og jeg tager den anden.

Veninde means female friend.

Danish distinguishes:

• ven = a male friend, or sometimes just friend in a general sense
• veninde = a female friend

So Min veninde means my female friend.

For an English speaker, one important point is that veninde normally does not mean a romantic girlfriend. If you mean girlfriend in the romantic sense, Danish usually uses kæreste.

Because Danish uses the possessive directly before the noun:

• min veninde = my female friend
• min bog = my book
• mit hus = my house

You do not normally add a separate definite article before a possessive in this kind of phrase.

So:

• correct: min veninde
• not correct here: den min veninde

Because pagaj is a common gender noun in Danish, so it takes en.

Danish nouns are usually either:

• common gender: take en
• neuter: take et

So:

• en pagaj = a paddle

This also matters later in the sentence, because that same noun is referred to with den in den anden.

Pagaj means paddle, the kind you use for something like a kayak or canoe.

Danish often distinguishes:

• pagaj = paddle
• åre = oar

A paddle is moved directly by the person holding it, while an oar is typically attached to a boat. So pagaj is the right word if the idea is that each person takes a paddle.

Tager is the present tense of tage, which usually means to take.

In this sentence, it can be understood as:

• takes
• picks up
• sometimes takes hold of

So:

• Min veninde tager en pagaj = My female friend takes/picks up a paddle
• jeg tager den anden = I take the other one

Because den anden means the other one.

The phrase refers back to pagaj without repeating the noun:

• Min veninde tager en pagaj, og jeg tager den anden
• literally: My friend takes a paddle, and I take the other

You could also say:

• jeg tager den anden pagaj = I take the other paddle

But since pagaj is already understood, Danish can leave it out and just say den anden.

Because it refers back to pagaj, and pagaj is an en-word.

So the matching form is:

• en pagaj
• den anden

If the noun were a neuter et-word, you would use:

• et hus
• det andet

So the choice between den and det depends on the gender of the noun being referred to.

Because anden is a bit irregular.

With many adjectives in a definite phrase, you often expect an -e form, but anden does not behave like a regular adjective in all forms. The common forms are:

• anden = other/second (common gender singular)
• andet = other (neuter singular)
• andre = other/others (plural)

So:

• den anden pagaj
• det andet hus
• de andre bøger

That means den anden is the correct form here.

Because og joins two main clauses, and the second clause keeps normal main-clause word order:

• jeg tager = I take

So the structure is:

• Min veninde tager en pagaj
• og jeg tager den anden

This is similar to English: My friend takes a paddle, and I take the other one.

Danish does often change word order when something else comes first, but not here, because the clause starts with the subject jeg.

Usually, yes, or at least it strongly suggests a pair or a choice between one and one other.

In this sentence:

• one person takes one paddle
• the speaker takes the other

That makes it sound like there are two relevant paddles in the situation.

If there were many paddles and you just meant another one, Danish might use a different wording depending on the context.

Yes, absolutely.

Both are natural:

• jeg tager den anden = I take the other one
• jeg tager den anden pagaj = I take the other paddle

The shorter version is common because the noun pagaj is already understood from the first clause.

You could say ven, but it changes the meaning slightly.

• Min veninde = my female friend
• Min ven = my male friend or sometimes just my friend, depending on context

So veninde is used because the sentence specifically identifies the friend as female. If that detail does not matter, Danish speakers might choose a different wording, but in this sentence it is part of the meaning.