Begge børn får lige meget juice.

Begge means both when you are talking about two people or things as one group: begge børn = both children.

Danish also has både ... og ..., but that is used to connect two separate items:

• Både Anna og Peter får juice = Both Anna and Peter get juice

In your sentence, begge is the natural choice because børn already gives you one plural noun phrase: both children.

Børn is the irregular plural of barn.

The forms are:

• et barn = a child
• barnet = the child
• børn = children
• børnene = the children

So this is just a plural form you need to learn as a vocabulary item. It does not follow the most regular plural pattern.

Begge børn is the normal, straightforward way to say both children.

You can also hear begge børnene, which is closer to both of the children and sounds a bit more specifically definite.

So:

• begge børn = both children
• begge børnene = both of the children

In simple statements like this one, begge børn is very natural.

Får is the present tense of at få, which often means to get or to receive.

So:

• barnet får juice = the child gets juice
• børnene får juice = the children get juice

In this sentence, får means get/receive.

Because Danish verbs do not change according to person or number in the present tense.

So Danish uses the same present-tense form with:

• jeg får = I get
• du får = you get
• barnet får = the child gets
• børnene får = the children get

This is simpler than English, where you have get but gets.

Danish main clauses usually follow the V2 rule: the finite verb comes in the second position.

In this sentence:

• Begge børn = first element
• får = second element

So the structure is correct:

• Begge børn får lige meget juice

If you move something else to the front, the verb still stays second:

• I dag får begge børn lige meget juice = Today both children get the same amount of juice.

Here lige meget means the same amount or equally much.

It is a very common Danish way to talk about equal quantity with things you do not normally count one by one, such as:

• juice
• vand = water
• tid = time
• penge = money

So Begge børn får lige meget juice means the two children receive an equal amount of juice.

Because juice is an uncountable noun.

In Danish:

• meget is used with uncountable or mass nouns
• mange is used with countable plural nouns

So:

• lige meget juice = the same amount of juice
• lige meget vand = the same amount of water
• lige mange æbler = the same number of apples

That is why meget is correct here.

Because juice is being used as a mass noun in a general quantity expression.

Danish often uses no article with uncountable nouns in this kind of structure:

• drikker vand = drinks water
• køber mælk = buys milk
• får juice = gets juice

The focus here is on how much juice, not on a particular juice. That is why plain juice sounds natural.