Vi må fjerne den gamle gren fra græsplænen.

In this sentence, må expresses necessity or obligation, so Vi må fjerne ... means We must remove ... or We have to remove ....

A few useful notes:

• må is the present tense of at måtte
• It often means:
  • must / have to
  • sometimes may / be allowed to, depending on context

So Danish må can be a little tricky because it covers meanings that English separates.

Examples:

• Jeg må gå nu = I have to leave now
• Må jeg komme ind? = May I come in?

In your sentence, the context clearly gives the must / have to meaning.

Because after a modal verb in Danish, the next verb normally stays in the infinitive without at.

Here:

• må = modal verb
• fjerne = infinitive

So:

• Vi må fjerne den gamle gren ... = correct

Not:

• Vi må at fjerne ... = incorrect

This works like other Danish modal verbs too:

• Jeg kan svømme = I can swim
• Du skal læse = You must read
• Han vil spise = He wants to / will eat

So a useful rule is:

modal verb + infinitive without at

Because when an adjective comes before a common-gender noun with den, the adjective usually takes -e.

So:

• gren = branch
• en gren = a branch
• den gamle gren = the old branch

Here:

• den marks the noun as definite
• gamle is the adjective form used here
• gren stays in its basic noun form

Compare:

• en gammel gren = an old branch
• den gamle gren = the old branch

This -e form is very common in definite noun phrases:

• den store bil = the big car
• det lille hus = the small house
• de røde blomster = the red flowers

Because Danish has two common ways to make nouns definite, depending on whether there is an adjective.

1. Without an adjective, Danish usually adds the definite ending:

   • gren = branch
   • grenen = the branch

2. With an adjective before the noun, Danish usually uses a separate definite word:

   • den gamle gren = the old branch

So you usually say:

• grenen = the branch but
• den gamle gren = the old branch

This is a very important pattern in Danish.

More examples:

• bilen = the car
• den røde bil = the red car

Because græsplænen has no adjective, so Danish uses the definite ending on the noun itself.

Breakdown:

• en græsplæne = a lawn
• græsplænen = the lawn

But in den gamle gren, there is an adjective (gamle), so Danish uses:

• den
  • adjective + noun

So the difference is:

• the lawn → græsplænen
• the old branch → den gamle gren

If you added an adjective to græsplænen, it would change too:

• den grønne græsplæne = the green lawn

Fra means from.

So:

• fra græsplænen = from the lawn

It shows where the branch is being removed from.

The structure is very similar to English:

• remove the branch from the lawn
• fjerne grenen fra græsplænen

A few similar examples:

• tage bogen fra bordet = take the book from the table
• flytte stolen fra vinduet = move the chair away from/from by the window

So in your sentence, fra marks the place the branch is being taken away from.

This is the normal Danish word order for a main clause:

subject + finite verb + infinitive/object/etc.

Here:

• Vi = subject
• må = finite verb
• fjerne = infinitive
• den gamle gren = object
• fra græsplænen = prepositional phrase

So the sentence is built very naturally:

• We
  • must
    • remove
      • the old branch
        • from the lawn

Danish and English are quite similar here.

One thing to remember: in Danish main clauses, the finite verb usually comes in the second position. That is true here:

• position 1: Vi
• position 2: må

Yes, you could, but the meaning changes a little.

• Vi må fjerne ... often means We must / have to remove ...
• Vi skal fjerne ... also often means We must / are supposed to remove ...

The difference is often about nuance:

• må can sound more like necessity, requirement, or something unavoidable
• skal can sound more like instruction, plan, duty, or intention

In many everyday situations, both are possible, but they are not always perfectly interchangeable.

Very roughly:

• Vi må fjerne den gamle gren = We have to remove the old branch
• Vi skal fjerne den gamle gren = We are supposed to / need to remove the old branch

Context decides the best choice.

Many learners find græsplænen difficult because it has Danish vowels and the soft d is not present to guide pronunciation like in some other words.

A rough English-friendly guide is:

• græs sounds a bit like gress, but with a Danish vowel
• plæne has a vowel somewhat like eh / ai depending on accent and how you hear it
• græsplænen is roughly GRESS-pleh-nen as a very approximate guide

But be careful:

• English spelling guides are only approximate
• Danish vowels are often quite different from English ones

Break it up like this:

• græs
• plæne
• -n definite ending in græsplænen

If useful, the noun is:

• en græsplæne = a lawn
• græsplænen = the lawn

Yes, fjerne is a common and useful verb. It means remove, take away, or sometimes eliminate, depending on context.

In physical contexts:

• fjerne en gren = remove a branch
• fjerne støv = remove dust
• fjerne pletter = remove stains

In more abstract contexts:

• fjerne et problem = remove a problem
• fjerne noget fra listen = remove something from the list

Related word:

• fjern = distant / remote in some contexts, though that is a different use

So fjerne is a good general verb for removing something.

Gren is a common-gender noun, so it takes en:

• en gren
• grenen
• den gamle gren

Unfortunately, there is no single rule that lets you always predict whether a Danish noun is en or et. You usually have to learn the gender together with the noun.

So it is best to memorize nouns like this:

• en gren
• en græsplæne

not just:

• gren
• græsplæne

That way you automatically know how to build other forms:

• en gren → grenen → den gamle gren
• en græsplæne → græsplænen → den grønne græsplæne

A practical tip: Always learn Danish nouns with their article.